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n 


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The  copy  filmed  hare  has  been  reproduced  thank* 
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L'exemplaire  film*  fut  reproduit  grflce  A  la 
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University  of  {Manitoba 
Winnipeg 


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fii-raga. 


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papier  est  imprimte  sont  filmAs  en  commenpant 
par  le  premier  plat  et  en  terminant  soit  par  la 
dernlAre  page  qui  comporte  une  empreinte 
d'impression  ou  d'iliustration,  soit  par  le  second 
plat,  selon  le  cas.  Tous  les  autres  exemplaires 
originaux  sont  filmis  en  commenpant  par  la 
premiAre  page  qui  comporte  une  empreinte 
d'impression  ou  d'iliustration  et  en  terminant  par 
la  darni4re  page  qui  comporte  une  telle 
empreinte. 


The  last  recorded  frame  on  each  microfiche 
shall  contain  the  symbol  ^*-  (meaning  "CON- 
TINUED"), or  the  symbol  V  (meaning  "END"), 
whichever  applies. 


Un  des  symboles  suivants  apparaltra  sur  la 
derniAre  image  de  cheque  microfiche,  selon  le 
cas:  le  symboia  — »>signifie  "A  SUIVRE",  le 
symboie  V  signifie  "FIN  ". 


IMaps,  plates,  charts,  etc.,  may  be  filmed  at 
different  reduction  ratios.  Those  too  large  to  be 
entirely  included  in  one  exposure  are  filmed 
beginning  in  the  upper  left  hand  corner,  left  to 
right  and  top  to  bottom,  as  many  frames  as 
required.  The  following  diagrams  illustrate  the 
method: 


L  s  cartes,  planches,  tableaux,  etc.,  peuvent  Atre 
filmto  A  des  taux  de  reduction  diffArents. 
Lorsque  le  document  est  trop  grand  pour  Atre 
reproduit  en  un  seul  clichA,  ii  est  film*  A  partir 
de  Tangle  supArieur  gauche,  de  gauche  i  droite, 
et  de  haut  en  bas,  en  prenant  le  nombre 
d'images  nAcessaire.  Les  diagrammes  suivants 
illustrent  la  mAthoda. 


1 

2 

3 

1 

2 

3 

4 

5 

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MICROCOPY   RESOLUTION   TEST   CHART 

(ANSI  and  ISO  TEST  CHART  No    2) 


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_J     /APPLIED  IIVHGE 


'65J   East    Mom    Street 

(716)   «82  -0300-  Phone 
(716)   288-  5989  -Fox 


An  Introduction 


to 


Modern  Logic 


BY 


RUPERT  CLENDON  LODGE,  M.  A. 

ASSISTANT    PROFESSOR   OF    PHILOSOPHY 
IN  THE  UNIVERSITY  OF  MINNESOTA. 

SOMETIME  JOHN  LOCKE  SCHOLAR  IN  MENTAL  PHICOSOPHY 
IN  THE  UNIVERSITY   OF  OXFORD. 


THE  PEKINE  IJOOK  COMPANY 
Minneapolis. 


An  Introduction 


to 


Modern  Logic 


BY 


RUPERT  CLENDON  LODGE,  M.  A. 

ASSISTANT  PROFESSOR  OF    PHILOSOPHT 
IN  THE  UNIVERSITY  OF  MINNESOTA. 

SOMETIME  JOHN  LOCKE  SCHOLAR  IN  MENTAL  PHILOSOPHT 
IN  THE  UNIVERSITY  OF  OXFORD. 


THE  PERINE  BOOK  COMPANY 
Minneapolis. 


PRKFACK 


TiiiH  book  ia  intended  to  be  precisely  what  the  title  impliei 
— an  introduction  to  modern  logic.  By  "modern"  logic  li 
understood  that  body  of  logical  theories  and  methods  which  is 
usually  associated  with  the  names  of  Lotze,  Sigwart,  Bradley,  ? 
Bosanquet,  Wundt,  Erdmann,  and  Dewey.  The  writer  has 
endeavored  to  place  himself  in  the  center  of  this  movement 
taken  as  a  whole,  and  to  set  forth  the  characteristic  doctrines 
of  the  modern  school,  so  far  as  this  has  seemed  possible  in  a 
book  which  is  professedly  introductory.  The  traditional  or 
Aristotelian  logic,  which  has  played  so  great  a  part  in  the 
past  history  of  thought,  is  entirely  omitted  from  consideration, 
as  are  also  symbolic  logic  and  the  various  attempts  at  invent- 
ing a  logical  calculus.  For  all  such  omissions,  as  well  as  for 
what  is  included,  the  sole  Justification  is  the  nature  of  an 
introductory  treatise.  It  has  seemed  best  to  avoid  polemics  — 
on  the  one  hand,  and  an  unmanageable  multiplicity  of  hypoth- 
eses on  the  other,  in  favor  of  a  certain  singleness  of  purpose  . 
and  organic  unity  of  thought. 

The  exercises  and  suggestions  for  further  reading  at  the 
end  of  the  different  chapters  should  be  regarded  as  an  integral 
portion  of  the  book.  To  attempt  to  study  logic  without  work- 
ing one's  way  through  appropriate  exercises  is  like  trying  to 
study  mathematics  without  solving  problems,  and  leads  inevit- 
ably to  a  certain  superflciality  of  mental  grasp  which  it  is 
the  avowed  aim  of  logical  treatises  to  light  and  destroy.  So 
also  to  confine  one's  reading  to  a  single  text-book  is  to  shut 
one's  mind  to  the  Interest  and  infinite  variety,  as  well  as  to 
the  concreteness  and  usefulness,  of  an  Important  branch  of 
modern  science. 

The  writer's  obligations  are  too  numerous  to  mention.  The 
influence  of  Plato  and  Kant,  on  the  one  hand,  and  of  Locke, 
Hume,  and  Mill,  on  the  other,  is  sufficiently  obvious.  But  in 
the  case  of  more  recent  writers  and  teachers  it  would  be 
Invidious  to  single  out  any  one  group.  The  chapter  headings 
of  Part  III  are  in  large  part  taken  from  Wundt's  AUgemeine 
MethodenJehre,  but  for  the  contents  of  the  chapters  in  question 
Wundt  is  in  no  special  sense  responsible. 

University  of  Minnesota. 
September,  1918. 


7 


SYNOPSIS 

Chapter 
Part  I 

JUDGMENT 

The  elements  and  chief  atages  of  judgment I 

The  sensory  element  In  Judgment II 

Sensory  Talidity  in  Judgment Ill 

The    intellectual    element — identity,    difference, 

and  organisation IV-VIII 

Intellectual  validity  in  Judgment IX 

General  validity — theory  of  Judgment X 

Pabt  II 

INFERENCE 

General  characteristics  of  inference XI 

(a)  dependent  or  hypothetical XII 

(b)  analytical  and  expansive XIII 

(c)  novelty-seeking  XIV 

(d)  constructive  and  systematic XV 

Sensory  and  intellectual  elements  in  Inference. .  XVI 

Validity — theory  of  inference XVII 


Pabi-  III 

SCIENTIFIC  mTROD 

Jifethodi  of  inveatigstlcm,  and  forms  of  exposi- 
tion    

(a)  Analyslf  and  synthesis XIX-XXI 

(b)  Abstraction  and  determination XXII-XXIII 

(c)  Induction  and  deduction XXIV-XXVI 

(d)  DeflnlttoB  ;. XXVII 

(e)  Classification  XXVIII 

(f)  Proof  XXIX 

(g)  Fallacy    XXX 

(h)  System  of  tlk«  acltnees XXXI 

Theory  of  scientific  meUiod XXXII 

vii 


CONTENTS 


INTRODUCTION  Page 

The  logical  attitude  of  mind— The  study  of  logic— Pre- 
liminary definition  of  logic 


PART  I 

Chapter  I 

JUDGMENT 

The  simplest  Judgments — The  elements  of  judgment- 
The  chief  stages  of  Judgment 


Chapter  II 

The  sensory  element — In  Judgments  of  perception — In 
Judgments  of  experience — In  symbolic  Judgments — In 
transcendent  Judgments — Summary 17 

Chapter  III 

The  question  concerning  sensory  validity — In  Judgments 
of  perception — In  Judgments  of  experience — In  sym- 
bolic Judgments — In  transcendent  Judgments — Con- 
clusion    23 

Chapter  IV 

The  intellectual  element — In  Judgments  of  perception — 
In  Judgments  ot  experience — In  symbolic  Judgments 
— In   transcendent  Judgments — Conclusion      ...      37 

Chapter  V 

Identity  or  sameness — In  Judgments  of  perception — In 
Judgments  of  experience — In  symbolic  Judgments — 
In  transcendent  Judgments — Conclusion     ....       46 

Chapter  VI 

Difference — In  Judgments  of  perception — In  Judgments  of 
experience — In  symbolic  judgments — In  transcendent 
Judgments — Conclusion        54 

ix 


X 


CONTENTS 

CHAFfEB  YII 


Page 


Internal  organisation— In  Judgments  of  perception— In 
Judgments  of  experience — In  symbolic  Judgments — In 
transcendent  Judgments — Conclusion 65 

Chapter  VIII 

External  organisation — In  judgments  of  perception — In 
Judgments  of  experience— In  symbolic  Judgments — In 
transcendent  judgments — Conclusion 79 

Chapteb  IX 

The  question  of  intellectual  validity — In  Judgments  of  per- 
ception—In Judgments  of  experience— In  symbolic 
Judgments— In   transcendent  Judgments — Conclusion      92 

Chapteb  X 

The  problem  of  general  validity — Idealism— Sensualism 

—The    solution— Application— Theory    of    Judgment    101 


Appendix 
Is  negation  subjective?— Is  negation  indefinite?  . 


108 


PART  II 

Chapteb  XI 

INFERENCE 

The  general  characteristics  of  inference — Dependence — 
Analytic  expansion — Novelty — Systematic  construc- 
tiveness — Conclusion 119 

Chaptfb  XII 

Dependent  or  hypothetical  nature  of  inference — Kinds  of 
dependence — From  cause — From  absence  of  cause — 
From  effect — ^From  absence  of  effect — Conclusion — 
Further  consideration — Concluslcn  conmrning  em- 
pirical cases— Hypothetical  versus  categorical— Con- 
cluding summary 127 


CONTENTS 
Chaptcb  XIII 


XI 

Page 


Greneral  nature  of  analysis  in  inference — Specific  features 
of  analysis — Analysis  and  intuition — Conclusion  138 


ChaftebXIV 

The  problem  of  novelty  in  inference — Sensory  novelty — 
Intellectual  novelty — The  field  of  relations-^Latent 
knowledge — Arguing   to   the   unknown? — Conclusion 


148 


Chapteb  XV 

Examples  of  systematic  constructiveness  in  Inference — 
Hpw  does  inference  construct? — ^Validity  of  infer- 
ential  constructions — Conclusion 


160 


Chapter  XYI 

The  problem  of  describing  inference — The  sensory  ele- 
ments— In  dependence,  analytic  expansion,  novelty, 
and  systematic  constructiveness — The  intellectual  ele- 
ments— In  dependence,  analytic  expansion,  novelty, 
and  systematic  constructiveness — Summary     .  .     169 

Chapteb  XVII 

The  problem  of  the  validity  of  inference — Dependence — 
Analytic  expansion  —  Novelty  —  Constructiveness — 
Theory  of  inference 184 


PART  III 

Chapteb  XVIII 
SCIENTIFIC  METHOD 

Scientific  and  unscientific  method — Methods  of  investiga- 
tion— ^Aaidysis,  abstraction,  determination,  synthesis, 
induction,  deduction — Summary— iForms  of  exposi- 
tion— Definition,  classification,  proof,  system  of  the 
sciences — Summary 197 


Xtl 


CONTENTS 
Chapter  XIX 


Page 


Nature  of  analysis — Aim  of  analysis — How  far  realisable? 
— With  man-made  structures  and  mental  models,  and 
with  natural  phenomena — Methods  of  scientific  analy- 
sis— Mathematical  and  causal— Validity  of  such 
methods — Summary 208 

Chapter  XX 

Nature  of  synthesis— Aim  of  syn  'lesls— How  far  realis- 
able?— With  mind-made  entitlf/-  and  with  natural 
phenomena — Methods  of  sclemiflc  synthesis — Mathe- 
matical and  causal — Validity  of  these  methods — 
Summary 218 

Chapter  XXI 

Analysis  and  synthesis — Is  analysis  synthetical?— Mind- 
made  entities,  and  natural  phenomena — Is  synthesis 
analytical?  —  Mind-made  entities,  and  natural 
phenomena — Summary — Differences  between  analysis 
and  synthesis — Apparent  starting-point,  conclusion, 
and  method — Is  synthesis  a  more  advanced  method? 
— Summary 230 

Chapter  XXII 

Nature  of  abstraction — Aim  of  abstratlon — How  far  real- 
isable?— With  mind-made  entities,  and  with  natural 
phenomena— Types  of  abstraction— Validity  of  these 
methods — Summary        243 


Chapter  XXIII 

Nature  of  determlnallon- Aim  of  determination — How  far 
realisable? — With  mind-made  entities,  and  with  na- 
tural phenomena — Validity  of  determination — Sum- 
mary— Abstraction  and  determination — Does  abstrac- 
tion Involve  determination? — Does  determination  In- 
volve abstraction? — Comparison  with  analysis  and 
synthesis 252 


CONTENTb 
Chapteb  XXIV 


XIII 

Page 


Nature  of  induction — Aim  of  induction — How  far  real- 
isable?— With  mind-made  entities,  and  with  natural 
phenomena— Types  of  inductive  method— Validity  of 
induction — Summary 263 

Chapter  XXV 

Nature  of  deduction — Aim  of  deduction — How  far  realis- 
able?— With  mind-made  entities,  and  with  natural 
phenomena — Types  of  deduction — Validity  of  deduc- 
tion— Summary 273 

Chapter  XXVI 

Induction  and  deduction — Does  induction  involve  deduc- 
tion?— Docs  deduction  involve  induction? — The  induc- 
tive-deductive method— The  nature  of  scientific 
investigation 283 

Chapter  XXVII   . 

Nature  of  definition— Aim  of  definition— How  far  realis- 
able?— With  mind-made  objects,  and  with  natural 
phenomena — Types  of  definition — Validity  of  deflni- 
tlo!i — Summary  and  conclusion 292 

Chapter  XXVIII 

Naturp  of  classification — Aim  of  classification — How  far 
realisal)le?— With  mind-made  entities,  and  with 
natural  phenomena— Types  of  classification — Validity 
of  classification — Function  of  classification  in  exposi- 
tion— Summary 305 


Chapter  XXIX 

Nature  of  proof— Aim  of  proof— How  far  realisable? 
— With  mind-made  entities,  and  with  natural  phe- 
nomena— ^Validity  of  proof — Types  of  proof — Sum- 
mary       316 


xiv 


CONTENTS 
CHAPnaXXX 


Page 


Definition  of  fallacy— Occasions  of  fallacy— Scope  of  fal- 
lacy—Source of  fallacy— Types  of  fallacy  ....     326 

Chapteb  XXXI 

Nature  of  a  system  of  the  sciences — Alra  of  such  system- 
atisation — How  far  realisable? — ^Types  of  liUch  sys- 
tematisation — ^Validity  of  such  systematlsation — 
Summary 33g 

Chapteb  XXXII 

Description  of  scientific  method — Sensory  elements  in 
scientific  method — Intellectual  elements  in  scientific 
method— Summary — ^Validity  of  scientific  method— 
In  dealing  with  mind-made  entities,  and  with 
natural  phenomena — Conclusion 346 

Index  I 355 

Index  II 357 


-< 


u 


'^\  -   P^  INTRODUCTION 

/- 

The  Logical   Attitude  of  Mind.— The  natural  behavior  of 
men,  as  of  other  animals,  Is  not  logical,  but  Instinctive.    We 
tend  to  react  to  most  of  the  concrete  situations  of  life  in  a 
way  determined  by  Inherited  neural  dispositions  rather  than 
by  "reasoning  things  out."    The  life  of  most  men  appears  to 
be  spent  in  acquiring  food  and  shelter,  a  family,  and  money 
to  expend  In  purchasing  houses,  automobiles,  education  and 
luxuries  for  the  rising  generation,  and  insurance  against  dis- 
aster.    That  Is  to  say,  the  main  outlines  of  life— power,  love, 
and  protection  of  the  family— are  fixed  in  the  main  by  Inher- 
ited racial  tendencies,  and  It  is  around  these  that  almost  all 
our  activities  are  grouped.     And  it  is  not  only  the  ouUines 
which  are  instinctive.    Nearly  all  our  more  detailed  every-day 
experiences  are  of  the  same  kind.     Taking  meals,  sleeping, 
feeling  aggressive  or  timid  In  our  work  and  play,  day-dream- 
ing as  we  plan  for  the  morrow,  feeling  elated  or  depressed  at 
the  progress  we  are  making— all  these  experiences  are  funda- . 
mentally  Instinctive,  and  we  should  be  seriously  pusiled,  ir 
we  were  called  upon  to  account  for  them  In  purely  rational 
terms.    To  the  average  man.  Indeed,  It  never  even  occurs  to 
make  any  such  enquiry.    "He  eats  because  the  food  tastes  good 
and  makes  him  want  more.    If  you  ask  him  why  he  should 
wani  to  eat  more  of  what  tastes  like  that,  he  will  probably 
laugh  at  you.    The  connection  between  the  savory  sensation 
and  the  act  It  awakens  Is  for  him  absolute  and  »e/6«ft7ei«Wnd- 
Hcft,  an  a  priori  synthesis  of  the  most  perfect  sort,  needing  no 
proof  but  Its  own  evidence.    To  the  metaphysician  alone  can 
such  questions  occur  as:    Why  do  we  smile,  when  pleased,  and 
not  scowl?    Why  a:e  we  unable  to  talk  to  a  crowd  as  we  talk 
to  a  single  friend?    Why  does  a  particular  maiden  turn  our 
wits  so  upside  down?     The  common  man  can  only  say,  '0/ 
courne  we  smile,  r/  course  our  heart  palpitates  at  the  sight  of 
a  crowd.  0/  course  we  love  the  maiden,  that  beautiful  soul  clad 
in  that  perfect  form,  so  palpably  and  flagrantly  made  from  all 
eternity  to  be  loved!'  "i 


•  r  M.-7^ 


^^1  William  James,  Principlea  of  Psycholoov.  chapter  xxiv.  pp.  886- 


INTRODUCTION 


Thus  we  see  that  not  only  the  mainspring*  of  bebarlor,  but 
alio  the  moulds  which  shape  and  direct  our  multifarious  partic- 
ular activities  are.  in  the  end,  animal,  racial,  instinctiTe.  The 
mind  is  no  receptive  waxen  tablet  on  which  any  and  every 
element  of  the  physical  world  can  equally  impress  it§  sensory 
Image.  We  see  and  hear  only  what  attracts  our  attention;  we 
notice  only  what  awakens  our  interest  and  stimulates,  directly 
or  indirectly,  those  dispositions  developed  in  the  long  course 
of  evolution,  which  we  call  instincts.  In  fact,  so  large  a  part 
do  instinct  and  habit  play  in  our  lives,  that  it  Is  seriously 
maintained  by  a  great  psychologists  that  man  seldom  reasons 
and  that  other  animals  never  reason. 

But  while  the  behavior  of  men  is  naturally  Instinctive,  it  is 
sometimes  forced  by  circumstances  to  be  something  more. 
The  insects,  it  is  true,  live  a  life  almost  purely  instinctive;  but 
then,  the  problems  which  they  have  to  face  are  almost  unvary- 
ing, so  that  one  bard  and  fast  chain  of  instincts  can  advantage- 
ously direct  the  honey-comb  construction  of  the  Mason  bee, 
or  the  egg-laying  activities  of  the  solitary  wasp  or  Yucca  moth. 
Our  human  problems,  however,  are  far  too  unstable  and  novel. 
No  inherited-  disposition  could  keep  pace  with  the  enormous 
changes  which  have  come  over  civilized  life  w^ithin  the  last 
two  generations;  and  even  within  the  brief  span  of  one  gener- 
ation, our  habits  need  to  be  readjusted  and  remodeled,  again 
and  again.  There  is  thus  in  our  lives  something  more  than 
instinct  or  habit,  something  continuously  readjusting,  re-shap- 
ing our  ways,  forever  solving  problems  forever  aew,  inventive, 
creative— in  a  word,  what  we  call  intelligence,  thought,  or 
reason. 

How  is  this  done?  How  does  intelligence  re-shape  our 
lives?  How  does  thought  add  moral  or  economic  cubits  to 
our  stature?  How  does  reason  enable  us  to  lead  lives  more 
nearly  approaching  the  ideal?  Let  us  consider  briefly  some  of 
the  ways  by  which  w^  rise  above  instinct  and  habit  One  of 
these  is  definition,  fixing  the  meaning  of  an  idea  in  such  a 
way  that,  amid  all  the  changes  and  chances  of  our  fluctuating 
experience,  we  hold  fast  to  that  one  meaning,  that  one  direc- 
tion of  our  thought.  Another  is  analyaia,  the  splitting  up  some 
complex  whole  into  parts  so  simple  that  we  can  readily  appre- 
hend their  nature,  and  readily  grasp  the  plan  of  the  whole 


awilhelm  Wnndt. 


/ 


LOGICAL  ATTITUDE  j 

constructed  out  of  lucb  part..  Yet  another  !•  inference  or 
reaeonlnf.  with  all  lU  various  forms,  by  which  from  a  dTon 
situation  we  construct  mentally  the  probable  consequence,  or 
antecedents,  and  generally  enlarge  our  menui  horlson  and 

the  Indispensable  handmaid  of  efficiency  and  success  In  com' 

n^vm  !^"*=*"*'°'  "«»  '°  *"  the  organised  institutional 
activities  of  the  present  day. 

The  logical  attitude  of  mind.  then.  Is  concerned  with  thai 
JO  utlon  Of  problems,  the  bridging  of  gaps,  the  removal  oL 
inconsistencies  and  inefficiencies.  In  cases  where  instinct  and 
habit  alone  would  be  insufficient.    There  Is  none  of  the  "of- 
course-ness"  of  instinct  about  this  mental  attitude.     It  1. 
reasoned,  deliberate,  thought-out  activity.    It  has  al«>  none  of 
he<  warmth  and  immodiacy.  and  none  of  the  vagueness  and 
confusion,  of  feeling.    It  is  calculaUng.  cool.  calm,  clear-^t 
precise;  deals  little  in  promise,  and  much  In  proofstuSe' 

LTbnt*"'  ""f  ^"  """°~"'  ''^•"•^«»  "»  <»'••''"'«  con r 
sions.  but  succeeds  broadly  and  Inevitably  m  the  end;  ^and  is 

riior,m  "S   ;  **'"•  ^*"*^°'  •*•  """'"»«  *«•»•'  m  the  final- 
rationality  of  the  universe. 

atHt*;rH**!"'L*'  '-*»'*-Th«  value  of  cultivating  such  a  mental 
a  tltud..  )B  beyond  question.    Without  i*.  much  of  our  art  and 

wLm       '  ''''  ''°"''*  disappear;    the  religion  of  ApoUo 

Hnd  Old  Night  would  come  again.    But  how  to  cultivate  this 
n  question.    Plato  reasoned  sublimely  before  Aristotle  wrote 

loenlr  h    *'■  '"'  r"*  °'  ""'■  '°'-«"°»*  •«='«"^'-t-  »»*ve  lever 
opened  the  pages  of  our  logical  manuals.    And  we  must  con- 

does  this  make  us  mathematicians-or  logicians?    If  we  study 

be  logic  of  the  emotions,  does  this  teach  us  to  l7-^rt 

reason  ourselves  out  of  feeling?     if  we  study   theTi^caJ 

oMh?  ^h^^'""  r^*^*'  '""•  *^'-  «•-  "«  Pracucal  i" 
of  the  subject-or  theoretical  mastery  of  the  principles'    Com 

mon  «»nse  and  a  wide  experience  of  men  come    o  4e  «me 

S  o?  Pe.  "  *"  '^'"  '°°"°  ^''^^  *^--«->  master,  in  th^ 
field  of  Pedagogy-men  like  Kant  and  PestaloMl-niometlme. 
make  poor  teachers;  and  authorities  In  the  field  oTZtheZ 
Z  «.f  ?  ^^^^'^'^^^  "«-«ve  artists.  To  put  it  brTefly  « 
the  attitude  comes  without  studying  the  theorj.  and  If  mLte.^ 


INTRODUCTION 


11 


I: 


of  th«  th«ory  1«  coniUtent  with  almoat  toUl  abMnc«  of  th« 
practical  attitude,  what.  If  any.  It  th«  value  of  itudylDf  loflcT 
To  thli  Quettlon  there  are  two  anawert.    The  flrat  »Mwer 
It  given  by  Hegel,  Botanquet.  and  many  other  wrltert  In  the 
field  of  logic.    With  great  modetty  they  dltclalm  any  pract  ca 
value  for  their  ttudy.  and  attign  to  It  only  that  theoretical 
value  to  which  any  pure  tclence  can  lay  claim.    If  we  dealre 
to  know  what  are  the  lawt  of  thought,  the  prlnclplet  on  which 
the  validity  or  correctneet  of  our  thinking  depend,  we  have 
at  much  right  to  ralte  tuch  queetlont  at  we  have  to  ttudy  pure 
phytlct  or  pure  mathematlca.     All  tuch  ttudlet.  like  meU- 
phytlct.  have  their  eufflclent  Juttlflcatlon  In  that  reaching  out 
after  knowledge  aa  tuch,  which  It  fundamental  In  our  human 
nature,  even  apart  from  practical  valuea.    There  It  a  tatltfac- 
Uon  in  knowing,  quite  apart  from  the  quettlon  of  uting  our 
knowledge;  and  many  loglclant  are  content  to  leave  on  one 
aide  the  quettlon  of  ute.  In  their  certain  enjoyment  of  that 
aatltfactlon  which  comet  from  finding,  discovering,  knowing. 
It  It  pottlble.  however,  to  antwer  the  quettlon  differently. 
While  it  It  true  that.  In  Its  higher  branches   'iglcal  study  It 
somewhat  remote  from  every-day  concernt,  s    ..  even  at  Ita 
deepest,  it  Intentlfies  and  quickens  our  vision,  of  Truth,  and 
justifies,  by  the  Insight  which  It  brings,  that  confidence  .n  the 
Intelligibility  of  things,  which  Is  fundamental  in  the  logical 
attitude  of  mind;  and  as  to  Its  more  elementary  branches--lt 
lit  merely  self-deception  If  we  suppose  that  there  was  ever  a 
great  scientist  who  was  not  also  a  good  logician.    Every  scien- 
tific  text-book  and  every  laboratory  course  lays  especial  weight 
on  questions  of  method,  methods  of  observation,  methods  of 
evaluating  results,  methods  of  establishing  conclusions.    But 
these  methods  are  not  peculiar  to  physics  or  biology  as  such 
They  belong  to  the  general  theory  of  method,  which  Is  a  branch 
of  logic.     Again,  the  researches  of  advanced  scientists,  on 
which  so  much  of  the  progress  of  knowledge  depends,  are 
almost  ilways  Investigations  to  test  the  validity  of  Inferences, 
the  theoretical  value  to  be  assigned  to  conclusions,  perhaps 
even  to  the  theoretical  assumptions  underlying  scientific  rea- 
soning    All  these,  however,  fall  within  the  province  of  logic. 
The  simple  truth  of  the  matter  Is  this;  a  little  experience,  a 
lltUe  common  sense,  enables  each  one  of  us,  as  we  say,  to 
reason  correctly,  whether  we  have  studied  technical  logic  or 
no-  and  so  long  as  we  move  only  within  the  more  elementary 


1/ 


STUDY  OF  LOGIC  5 

reaches  of  experience,  our  common  Mnae  itandardi  of  truth 
»re,  perhaps,  sufflclent.  But  lf_jEe-«lah_to.xiiMLOurse]Tei  ^  ^ 
beyond  thiM  elemtotary  and.  limited  i^bere;  if  we  wish  to  ■  ^ 
think  clearly  and  consecutively  in  ofBer  to  reach  conclusions 
aboTe  the  level  of  mere  common  sense;  if  we  wish  to  acquire 
business  efflclency,  or  to  succeed  beyond  the  average  in  life 
or  in  science,  we  need  to  withdraw,  for  a  season,  from  the 
more  active  concerns  of  mere  living,  and  r»flect^|irefully  and 
systematically  on  the  principles  and  methods  oTflght  thinking. 
Then,  having  acquired  some  grasp  of  the  theory  beyond  what  | 
the  average  man  knows  or  •uspects,_wo^caiuU!pl7  our  d^pfg  L 
Inslght  In  order  to  attain  a  higher,  level  of  efflflancy  and  suc-~y 
cesa  than  Is  possible  without  such  reflection;  and  In  order  to  | 
cultivate  the  best  fruits  of  the  logical  attitude  of  mind.  It  Is  \ 
necessary  to  make  ourselves  thoroughly  familiar  with  the  prin-  ) 
clples  and  methods  of  right  thinking— In  a  word,  to  study  / 
logical  theory.  "^ 

Preliminary  Definition  of  Logic— Logic,  then,  is  tha 
study  of  thought— systematic  reflection  on  the  principles 
and  methodf  ot  xig&l  (filUIUl?. — THmiaJfement  is  cor- 
reCCTTWl  fs  not  sulBciently  precise  to  serve  as  a  sclentiflo 
definition  of  logic.  Psychology,  for  instance,  includes  a 
'tiidy  of  the  thought-processes,  and  to  some  extent  deals  with 
the  methods  of  right  thinking.  Is  logic,  then,  a  branch  of 
psychology?  If,  as  its  name  Implies,  psychology  were  studied 
as  the  general  science  of  mind,  or  the  general  science  of 
behavior,  it  would  Include  the  study  of  logical  behavior  or 
right  thinking,  and  logic  would  certainly  be  a  department  of 
psychological  investigation.  But  in  pn-sent  day  practice, 
psychologlgts  tend  to  regard  their  science,  not  as  the  general 
science  of  mind  or  behavior,  but  as  one  special  mental  science; 
and  while  they  do  study  logical  behavior,  they  do  so  In  a  very 
restricted  way,  and  from  a  viow-point  entirely  different  from 
that  taken  by  logic. 

Let  ws  consider  an  Instance.  Suppose  Mr.  A  to  have  recently 
become  a  member  of  the  Republican  party,  or  of  the  Congre- 
gational Church.  Psychological  explanation  of  this  change  of 
heart  would  lay  especial  emphasis  upon  the  various  elements 
In  Mr.  A'M  personal  history  and  environment  which  had  led 
him  to  take  the  step  In  question:  the  Influence  of  old  and 
new  associations,  the  weight  of  social  pressure,  the  greater 
appeal  of  the  new  opinions— what  he  would  himself,  perhaps. 


INTRODUCTION 


I 


A 


call  their  greater  reasonablenesa.  In  other  words,  the  view- 
point of  paychologlcal  explaiiation  is  genetic,  and  traces  the 
steps  in  his  personal  evolution  which  gradually  led  up  to  the 
change  in  question.  This  genetic,  historical  kind  of  analysis 
is,  however,  sharply  to  be  distinguished  from  logical  analysis. 
The  logical  analysis  of  this  conversion,  for  instance,  would 
consist  of  a  clear  setting  forth  of  the  arguments  pro  and  con. 
in  such  a  way  that  we  couW  see  the  greater  comprehensive- 
ness, consistency,  and  truth  of  the  new  opinions.  It  would  be 
concerned,  not  at  all  with  the  historical  side  of  the  thought- 
processes  as  such,  but  wholly  with  their  meaning,  with  the 
hanging  together  of  the  thoughts  in  a  consistent  system,  in 
accordance  with  the  standards  of  truth.  Whether  reasoning 
is  consistent  or  inconsistent,  whether  conclusions  are  true  or 
false,  no  psychology  can  tell  us.  Truth  and  consistency  are 
not  mere  matters  of  history  or  personal  evolution,  but  have 
their  own  standards  and  laws,  and  the  scientific  study  of  these 
laws  is  logic.  Psychology  deals  with  the  process-side,  logic 
with  the  valiigiJLxifllde^of  thojight. 

If,  then,  we  wish  to  mark  out  the  field  of  investigation  with 
a  preliminary  definition,  we  can  say:  logic  is  the  scientific 
study  of  the  laws  or  principles  on  which  tne  validity  of  right 
thinking  depends:  or,  more  briefiy,  logic  Is  the  study  of 
validity. 


FOR  FURTHER  READING 

A.  E.  Avery,  The  Pre  »nt  Day  Conception  of  Ix)glc :  PMlotophical 
Review,  Vol.  XXVII,  pp.  405-412.  B.  Bosanquet,  BanentiaU  of  Logic, 
pp.  1-34.  J.  Dewey,  Bsaays  in  Experimental  Logic,  pp.  1-74.  B.  Erd- 
mann,  Loglk,  (2nd  Edit.),  pp.  1-33.  E.  Husserl,  Logiache  Vnterauch- 
ttnacn.  pp.  3-8.  U.  Ix)tze.  Logic,  pp.  1-0.  Chr.  Slgwart,  Logic,  pp. 
1-2.     W.  Wundt,  Logik,  (3rd  Edit),  Vol.  I,  pp.  1-9. 


PART  I 
JUDGMENT  I 


,hl^t  S?"'^/i:"^^""^"*.'*'  "««d  'n  modern  logic,  In  order  to  emohaaiM 
sharply  the  difference  between  logic— which  studies  what  wptftriirS 

iSKip'^foVs'.,"'  "''^  r'"*l  nvingthoSght^andl!r\m^r!^wh^ 
studies  the  verbal  expression  of  thought      HIstorlcallT    «irfw>  iTm. 

JhXh^^'^.h'if*?  S'*?'""".^'  «>  .^'^''t  in  pface  «  an  iiiUyJis^^thrUTlM 


i/\ 


CHAPTER  I 

TYPICAL  STAGES  OF  JUDGMENT. 

The    8    iplest   Judgment*— In   every   scientific   study,   we 
start  with  the  simple  and  proceed  gradually  to  the  complex   a-  , 
Logical  study  also  starts  with  the  simple.    What.  thenjfl_tlie      ~ 
simplest  kind   of  valid  thlnkinf .  the  unit;  as  lt~were,  of 
^    thought?    Let  us  consider  an  example.    "It  the  sun  is  shining 
W3  will  go  to  the  woods;  but  if  it  is  wet,  we  will  stay  in  and 
read."      We  have  here  a  single  thought.    But  though  tingle 
it  is  obviously  not  what  we  should  call  simple,  but  is  evidently 
complex.    Let  us  analyse  it.  or  split  up  the  complex  thought 
into  simpler  parts.     "The  sun  is  shining";     "We  wiU  go  to 
the  woods":     "It  is  wet";     "We  will  stay  in";      "We  will 
read."     If  we  compare  each  one  of  these  brief  statements 
with  the  original  example,  we  see  at  once  that  they  are  much 
less  complex.    Let  us  further  compare  them  with  one  another 
"The  sua  18  shining"  and  "It  is  wet"  appear  to  belong  together! 
to  represent  two  forms  of  the  same  kind  of  Judgment.    Let 
U8  regard  them  as  one  group,  group  A.  Similarly  "We  will 
go  to  the  woods."  "We  will  stay  In."  "We  will  read."  seem 
to  express  one  and  the  same  kind  of  thought,  and  thus  to 
belong  to  a  "we  will"  group,   which  represents  a  kind  of 
thought  different  from  that  expressed  In  group  A.    Let  us  call 
the  "we  will"  group,  group  B.    The  thoughts  in  group  B  are 
judgments  of  purpose,  and  seem  more  complex  than  Judg- 
ments of  sense-perception  such  as  "The  sun  is  shining  "    We 
shall  therefore  regard  group  A,  i.  e..  Judgments  of  sense-per- 
ception, as  the  simplest  kind  of  Judgment  revealed  by  a  con- 
sideration of  our  example. 

Are  such  perceptual  Judgments,  however,  to  be  considered 
as  ultimate?  Are  they,  in  fact,  the  simplest  Judgments  we 
can  make?  Perhaps  we  should  draw  a  further  dIstlncUon 
It  is  wet.  for  instance,  might  be  thought  less  complex  than 
The  sun  Is  shining."  Perhaps  the  distinction  will  become 
plainer  if  we  compare  "It  Is  fine"  with  "The  sun  is  shining" 
and  "It  18  wet"  with  "The  rain  Is  heavy."    Many  loglclims 


ff 


10 


TYPICAL  STAGES  OF  JUDGMENT 


have,  in  fact,  regarded  such  impersonal  Judgments  at  the 
simplest  thoughts  we  can  have.2  It  seems  better,  however, 
to  speak  of  more  primitiTO  or  less  developed  forms  of  the 
same  type  of  judgment,  rather  than  of  greater  simplicity  or 
less  complexity.  "It  is  fine"  and  "The  sun  is  shining"  have, 
after  all,  substantially  the  same  meaning.  The  only  logical 
difference  is,  that  the  meaning  is  more  clearly  expressed  in 
the  more  developed  form.  We  shall  accordingly  take  as  the 
simplest  and  most  elementary  acts  of  thought  which  we  can 
discover.  Judgments  such  as  "This  is  red,"  "It  is  warm," 
"There  is  a  noise,"  "This  is  heavy,"  "That  tastes  bitter," 
"There  is  an  odor,"  etc. — i.  e.,  simple  Judgments  of  sense- 
perception. 

The  Elements  of  Judgment. — In  the  above  instances  we  have 
Judgments  so  simple,  that  here,  if  anywhere,  we  should  be 
able  to  pick  out  some  of  the  elements  upon  which  the  validity 
of  Judgments  depends.  In  cases  which  were  more  complex 
we  might  *e  unable  to  see  our  way.  But  in  these  simple 
cases,  if  anywhere,  we  should  be  able  to  discover  at  least  the 
more  obvious  elen-  ts.  Let  us  therefore  consider  these  Judg- 
ments of  perception  closely.  Can  we  discover  any  simple  fac- 
tors, any  constituent  elements  of  such  Judgments? 

Two  elements,  upon  which  perhaps  the  validity  of  Judgment 
depends,  we  can  discover  almost  at  once.  These  elements  are 
(a)  sensory,  and  (b)  intellectual,  (a)  All  Judgments  of  per- 
ception al^thongfits  about  something  present,  something  given 
to  us  in  perception,  given  to  us  through  the  senses,  stinsory. 
"This-red,"  "Warm-feeling,"  "Noise-here,"  "That-bltter-taste," 
etc.  It  may  be  that  all  Judgments  whatever,  and  not  merely 
perceptual  Judgments,  are  similarly  thoughts  about  something 
which  is,  in  the  end,  given  to  us  In  sensation.  In  this  case, 
all  thought  would  have  this  sensory  element,  and  the  func- 
tion of  sensation  would  be,  to  furnish  us  with  a  channel  by 
means  of  which  we  could  come  to  know  objects,  or  things- 
which-we-can-experlence.  (b)  On  the  other  hand,  so  far  as 
Judgments  of  perception  are  thoughts  about  something  pres- 
ent, they  undoubtedly  contain  an  element  which  we  should 
call  Intellectual.  This  Is  in  such  cases,  not  so  easily  noticed 
as  is  the  sensory  element.    In  order,  then,  to  bring  out  more 


2  For  a  rewnt  study  of  the  whole  Bubject  of  the  Impersonal  Judg- 
ment, see  8.  P.  Macljennan,  The  Impertonal  Judgment,  1897. 


ELEMENTS  OF  JUDGMENT 


11 


clearly  the  presence  of  the  Intellectual  element,  we  shall  pro- 
ceed to  take  a  number  of  slightly  more  developed  cases  of  per- 
ceptual Judgment.  "This  paper  is  red,"  "It  is  warm  near  the 
stove,"  "There  is  a  noise  at  the  door,"  "This  book  is  heavy." 
These  instances  are  all  perceptual,  but  we  can  at  once  observe 
that  certain  intellectual  elements  are  now  more  prominent. 
Instead  of  reference  to  the  undifferentiated  "this"  as  the 
sensory  given,  we  refer  to  the  paper,  stove,  door,  book,  etc., 
i.  e.,  to  determinate  objects,  the  recognition  of  which  involves 
distinction,  comparison,  classification,  etc.,  which  are  proc- 
esses predominantly  intellectual.  Let  us  further  consider  yet 
more  developed  perceptions.  "This  paper  is  a  brighter  red 
than  that,"  "It  is  warmer  near  the  stove  than  near  the  door," 
"This  book  is  heavier  than  that."  We  have  here  much  the 
same  general  sensory  elements  as  before.  But  we  now  have 
in  a  very  clear  and  explicit  form  the  Intellectual  act  of 
comparison.  "This  paper"  and  "That  paper"  are  held 
together  in  one  intellectual  act,  and  are  compared  in 
respect  of  their  brightness-value.  So  too  "Near  the  stove" 
and  "Near  the  door"  in  respect  of  their  warmth.  In  fact,  the 
more  highly  developed  such  judgments  become,  the  more 
plainly  can  we  observe  the  presence  of  intellectual  elements. 
But  in  the  very  elementary  and  primitive  cases  too  we  can 
now  see  tbe  presence  of  abstraction  and  recognition  at  least 
The  "This"  is  differentiated  into  red,  warm,  heavy,  etc.,  and 
these  are  not  only  clearly  apprehended,  but  are  apprehended 
in  distinction  from  one  another,  xu  other  words,  in  these 
simplest  of  all  judgments  there  is  present,  not  only  a  sensory, 
but  also  an  intellectual  element. 

Typical  Stages  of  Judgment. — With  the  sensory  element  in 
judgment,  logic  is  not,  as  a  rule,  much  concerned.  It  is  In 
epistemology  or  the  theory  of  knowledge,  that  the  function 
of  sensation  as  a  factor  In  knowledge  is  especially  studied,  and 
it  is  still  a  question  whether  the  theory  of  knowledge  should 
or  should  not  be  regarded  as  constituting  an  integral  part  of 
modem  logical  investigatlon.a  We  shall  therefore  postpone, 
for  the  moment,  further  discussion  of  the  sensory  factor  in 


sSchuppe  (Brkenntniatheoretitche  Logik),  Wundt,  and  Wlndelband 
fEnct/clopddie  der  philosophitchen  WUsenachafien,  Vol.  1)  regard  tiie 
thwry  of  knowledge  as  falling  wlthla  tlie  field  of  lo^ic.  ar  vice  versa. 
Erdmann  Incorporates  "co'  ..arlee"  from  the  theory  of  knowledge  la 
his  logical  Blementarlehre.  Bradley  and  Bomnquet  are  also  to  be 
reckoned  among  the  eplstemological  logicians. 


fir 


12 


TYPICAL  STAGES  OF  JUDGMENT 


judgment,  and  shall  consider  more  closely  the  intellectual 
factor. 

In  order,  however,  to  deal  with  the  intellectual  element  in 
judgment  in  any  adequate  way,  we  can  certainly  not  confine 
ourselves  to  elementary  perceptual  judgments.  It  is  no  longrer 
a  question  of  picking  out  the  least  complex  type  of  judgment 
in  order  to  avoid  obscurity,  and  in  order  to  enable  our  unac- 
customed eyes  to  see  their  way  in  a  simple  case.  We  have 
now  to  lace  the  more  general  problem  of  validity  in  judging 
as  such,  and  this  involves  consideration,  not  only  of  the  ele- 
mentary cases,  but  also  of  the  more  highly  developed  forms 
or  stages  of  judgment,  in  order  that  nothing  vital  may  be 
overlooked.  In  order,  then,  to  clear  the  way  for  our  whole 
subsequent  investigation  into  the  sensory  and  intellectual 
factors,  we  must  be  able  to  cover,  in  some  clear  and  brief 
way,  the  whole  field  of  judgment.  This  we  shall  do  by  arrang- 
ing different  kinds  or  stages  of  judgment  in  a  table,  starting 
with  the  more  elementary  and  proceeding  to  the  more 
advanced — i.  e.,  proceeding  from  judgments  in  which  the  intel- 
lectual element  is  less  prominent  to  cases  in  which  it  is  more 
prominent. 


TABLE  OF  JUDGMENTS 

1.  Judgments  of  Perception. — E.  g.,  "This  room  is  warm," 
"This  oak  has  less  foliage  than  that  beech." 

2.  Judgments  of  Experience. — E.  g.,  "The  freight-trains 
passing  over  the  bridge  grow  more  troublesome  every  year," 
"Noise  is  usually  a  compound  of  tones." 

3.  Symbolic  Judgments. — E.  g.,  "Rome  was  occupied  by 
Caesar,"  "Strathcona  lies  on  the  North  Saskatchewan,"  (where 
the  evidence  is  not  direct  experience,  but  a  textbook  account 
of  a  place  we  have  never  seen).  So  too  "The  theory  of  the 
synapse  is  fundamental  for  the  explanation  of  conscious 
behavior"  (where  we  have  had  no  direct  experience  of  syn- 
apses). 

4.  Transcendent  Judgments. — E.  g.,  "God  is  a  substance 
consisting  in  Infinite  attributes,  of  which  each  expresses 
eternal  and  Infinite  essentiality,"  "Thlngs-in-themselves  are 
absolutely  unknowable,"  "True  evolution  is  the  progressive 
self-organisation  of  a  system  of  timeless  selves." 

Let  us  explain  briefiy  the  above  distinctions.     A  judgment 


TYPICAL  STAGES  OF  JUDGMENT 


13 


of  experience  differs  from  a  perceptual  judgment,  in  that  it 
depends  more  on  memory  of  previous  perceptions  than  on 
direct  present  perception.  It  is  more  deveJoped,  and  sums 
up  many  previous  experiences,  as  a  composite  photograph 
gives  us  the  result  of  many  direct  likenesses  of  actual  per- 
sons. For  instance,  "Most  writing-paper  is  white"  sums  up 
many  experiences  of  writing-paper,  and  while  on  the  one  hand 
less  direct  and  immediate  than  "This  writing-paper  before  me 
is  white."  on  the  other  is  more  advanced,  more  representative, 
more  Intellectual,  than  the  simple  perceptual  Judgment.  Still, 
even  in  the  perceptual  judgment  there  is  tome  appeal  to  pre^ 
vlous  experiences.  For  we  know  the  object  before  us  to  be 
"writing-paper"  and  "white."  The  distinction  between  ju«»«?- 
ment  of  perception  and  Judgment  of  experience  is  thus  not 
absolute,  but  is  a  question  of  more  or  less,  a  matter  of  degree. 
Where  the  sensory  element  predominates,  we  have  the  stage 
of  'adgment  which  we  call  judgment  of  perception.  Where 
the  mtellectual  element  plays  the  greater  part,  we  have  the 
judgment  of  experience. 

A  symbolic  Judgment  differs  from  a  judgment  of  experience, 
in  that  we  are  here  dealing  with  a  sort  of  extension  of  our 
experience,  based  indeed  on  previous  experiences,  but  con- 
structing, on  the  analogy  of  these  past  experiences,  new  objects 
of  slmUar  type,  objects  which  we  might  possibly  have  experi- 
enced, or  might  possibly  e.^perience  in  the  future,  but  which 
in  actual  fact  we  have  never  experienced.  Thus,  if  we  had 
lived  In  Rome  at  the  time  of  its  occupation  by  Caesar,  our 
thought  would  be  a  judgment  of  experience.  If  not,  indeed,  a 
perceptual  judgment  But  where  we  have  had  direct  experi- 
ence of  cities  differing  from  Rome,  and  can  only  constiuct 
for  ourselves  imperfectly,  in  the  light  of  very  Inadequate  past 
experience,  what  it  meant  for  a  city  to  be  occupied  In  war- 
time by  the  forces  of  Caesar,  our  Judgment  is  only  symbolical. 
The  less  directly  the  case  happens  to  be  related  to  our  per- 
sonal experience,  the  harder  do  we  find  it  to  spread  out  our 
experience  so  as  to  make  vivid  to  ourselves  scenes  so  remote 
from  what  we  have  seen  and  felt,  and  the  further  do  we  tend 
to  fall  short  of  full  realisation  of  the  meaning  of  our  Judg- 
ment.  We  have  the  bare  skeleton  of  experience.  The  flesh 
and  blood,  the  living  elements,  are  almost  totally  missing.  In 
such  Judgments,  while  the  sensory  elemeut  may  be  weak,  the 
intellectual  element  of  cor'^truction   is  far  more  prominent 


14 


TYPICAL  STAGES  OF  JUDGMENT 


than  in  Judgments  which  remain  contentedly  within  the 
circle  of  our  own  experience.  And  yet,  in  Judgments  of  experi- 
ence also  there  is  some  construction,  some  putting  together 
of  past  experiences  in  order  to  produce  something  new,  the 
composite  result  which — as  a  composite  unity,  at  any  rate — 
was  never  actually  experienced.  We  see  then  that  here  also 
the  difference  is  a  question  of  more  and  less,  a  matter  of  degree 
only.  Where  the  sensory  element  is  relatively  greater  and 
the  intellectual  construction  relatively  less,  we  have  a  Judg- 
ment of  experience.  Where  the  constructive,  intellectual 
element  decidedly  predominates,  we  have  the  symbolic  Judg- 
ment. 

The  transcendent  Judgment  differs  from  the  symbolic  Judg- 
ment, in  that  we  here  transcend  or  go  beyond,  not  merely 
our  actual  experiences,  but  also  even  possible  human  experi- 
ence. In  the  symbolic  Judgment,  our  subject  is  always  some- 
thing which  might  conceivably  be  experienced,  or  have  been 
experienced.  But  in  the  transcendent  Judgment,  the  subject 
could  never  be  experienced.  Where,  for  example,  our  experi- 
ence is  finite,  any  Judgment  about  the  infinite  transcends  the 
possibility  of  experience,  and  we  have  a  transcendent  Judg- 
ment. Such  Judgments  are  both  natural  and  common.  How 
natural,  or  rather  inevitable,  any  attempt  to  think  one's  way 
to  a  first  cause,  or  to  a  profound  and  satisfying  standpoint  for 
the  conduct  of  life  will  show.  How  common,  the  slightest 
reflection  on  human  mental  history  will  sufficiently  attest. 
CouBider,  for  example,  the  ever  recurring  interest  in  mysti- 
cism, the  medieval  search  for  the  philosopher's  stone,  the 
inventor's  fascination  in  the  case  of  perpetual  motion,  the 
still  not  uncommon  belief  that  one  can  read  destiny  by  the 
lines  in  the  palm  of  the  hand,  if  not  by  the  conjunctions  of 
the  heavenly  bodies.  The  "anticipations"  of  scientists — 
intended,  no  doubt,  as  symbolic  extensions  of  experience — 
teem  with  transcendent  Judgments.  Most  of  our  philosophi- 
cal theories,  much  of  our  moralising,  and  much  of  our  relig- 
ious thought  is  transcendent.  In  every  walk  of  life  the  human 
yearning  after  some  ineffable  ideal,  some  unspeakable  perfec- 
tion— the  "vision"  (as  we  call  it)  of  ideal  truth,  power,  love, 
or  happiness — ^leads  us  insensibly  and  inevitably  beyond  the 
narrow  confines  of  possible  experience. 

While  in  strict  theory  it  might  seem  as  though  transcen- 
dent Judgments  were  sharply  distinguished  from  symbolic  Judg- 


TYPICAL  STAGES  OF  JUDGMENT 


IS 


menti,  In  definite  cases  the  line  cannot  be  drawn  with  pre- 
cision. Transcendent  Judgments  contain  some  sensory  and 
experiential  elements,  and  symbolic  Judgments  contain  a  fair 
portion  of  that  Idealising  tendency  which  frees  the  imagina- 
tion from  the  fetters  of  actual  experience.  A  transcendent 
Judgment  is  thus  only  an  exaggerated  symbolic  Judgment,  and 
the  distinction,  here  also,  is  one  of  more  and  less.  Where  the 
Idealising  tendency,  the  intellectual  element,  is  more 
restrained,  we  have  a  symbolic  Judgment  Where  It  is  almost 
wholly  loosed  from  its  experiential  moorings,  where  the  sen- 
sory element  is  distinctly  less  prominent,  we  have  the  tran- 
scendent Judgment. 

The  above  stages  cover  the  whole  field  of  human  thought. 
They  represent  four  stages  of  judgment,  distinguished  from 
one  another  only  relatively,  according  as  the  perceptual  or 
the  Intellectual  element  predominates.     The  simplest  Judg- 
ments of  perception  exemplify,  to  some  extent,  the  operation 
of  the  elaborative.  ideallBlng  tendency  of  Intellect.    And  the 
most  transcendent  Judgments  we  can  make,  the  finest  thought- 
webs  we  can  spin,  are  still  attached  to  earth  by  some  sensory 
threads,  gilded  o'er  by  the  warmth  of  personal  feeling  and 
personal  sense-experience.    A  pure  Intellect  and  a  pure  sen- 
sation are  equally  beyond  our  human  thought.    All  our  think- 
ing moves  within  these  two  extremes,  and  partakes  of  both 
principles  in  varying  proportions.    It  may  be  that  some  prin- 
ciple yet  more  profound  remains  to  be  discovered.    But  the 
presence  of  these  two  principles— in  perceptual,  experiential, 
symbolic,  and  transcendent  Judgments  alike— is  certain,  and 
for  the  present  we  must  look  for  the  conditions,  on  which 
the  validity  of  all  Judgment  depends.  In  the  sensory  and  Intel- 
lectual  elements. 

FOR  rURTHER  READINO 

p«;.^ ■.  ^"^^'^T'  ''"  '^"•odttctor,,  Logic,  chapter  xxlll.     J.  Dewey. 
E,gav,  in  Ewpertmental  Logic,  pp.  183-219.     B.  Erdmann.  /^o«    (2nd 

nal  of  Philotophy,  etc..  Vol.  XV.  pp.  541-550. 

BXERCISE8 

nl^*Jl  whether  yt,u  can  diacover  any  judpnenU  .Jinpler  thap  Judg- 
^^.«  *»'  P^'^^P"""-     *'<>'•  l'»t.nee.   are  any  of  the  following  more 


ff 


16 


TYPICAL  STAGES  OF  JUDGMENT 


2.  Can  you  think  of  any  judgments  which  cannot  b*  clanad  aa 
perceptual,  experiential,  ■ymboilc,  or  transcendent — or  at  leaat  loine 
Cranaltlon-form  of  theie?  Try  to  claRsIfy  the  following,  arranging 
them  under  separate  heads,  as  (1)  perceptual.  (2)  experiential,  (3) 
symbolic,  (4)  transcendent:  Up  we  go  I  It  takes  thirteen  days  to 
get  from  here  to  Paris.  Everywhere  you  see  grain  eleTators.  Nero 
nddled  while  Rome  was  burning.  The  prince  now  possessed  the  magic 
sword,  the  cap  of  darkness,  and  the  seven-league  boots.  I  am  the 
master  of  my  fate,  I  am  the  captain  of  my  soul !  This  color-mixture 
of  yellow  and  blue  gives  gray.  A  thick  rug  under  the  feet  tends  to 
prevent  chllblalus.  You  can  buy  a  good  boat  for  |40.00.  Ilumpty 
Dumpty  sat  on  a  wall.  Seven  plus  five  equals  twelve.  O  king,  live 
for  ever !  The  hens  are  laying  more  eggs  than  ever  before.  Vou  are 
looking  pale.  These  weeds  are  choking  the  vegetables.  It  Is  sure  to 
rain  on  Thanksgiving  Day. 

3.  Go  over  your  classified  list  of  the  Judgments  given  In  the  pre- 
ceding exercise.  Can  some  of  the  experlent^l  Judgments  be  regarded 
as  perceptual?  Can  some  of  the  symbolic  Judgments  be  regarded  as 
experiential?  Can  some  of  the  transcendent  Judgments  be  regarded 
as  symbolic?  And  Is  there  an  experiential  element  even  In  Judgments 
of  perception?  Is  there  a  symbolic  element  even  In  the  Judgments  of 
experience?  Is  there  a  transcendent  element  In  the  symbolic  Judg- 
ments? Do  all  the  forms  pass  Into  each  other  by  eany,  and  almost 
Imperceptible,  gradations? 


CHAPTER  II 

THE  SENSORY  ELEMENT  IN  JUDGMENT. 

Th«  Sensory  Element.— In  order  to  study  the  sensory  ele- 
ment in  judgment.  It  would,  perhap..  be  convenient  If  we  could 
Isolate  It  and  examine  It  in  a  separate  case,  uncontamlnated 
by  any  admixture  of  foreign  elements.    But.  as  we  have  seen, 
the  sensory  element  is  never   found  alone;  no  Judgment  Is 
found  in  which  the  sensory  elements  are  not  shot  through 
and  through  with  intelligence,  organised  and  built  up  Into 
something  more  than  mere  blind  sensation.    The  most  that 
we  can  do.  If  we  wish  to  discover  the  valldlty-value  of  sensa- 
tion, is  to  consider  a  variety  of  cases,  neglecting  the  intel- 
ectual  element,  and  concentrating  our  mental  microscope  on 
the  part  played  by  sensation  In  giving  us  a  Judgment  on  whose 
validity  we  can  rely.    In  order  that  the  cases  considered  shall 
cover  the  whole  field  of  thought,  we  shall  make  use  of  the 
table  of  Judgments  established  in  the  last  chapter,  and  shall 
begin  with  Judgments  of  perception. 

(A)    In  Judgmento  of  Perception.— What  is  the  sensory  ele- 
ment  in  simple  Judgments  like  "This  is  warm."  "This  is 
green."  "This  is  hard."  "This  is  heavy,"  etc.7    On  the  one 
hand  we  have  a  reference  to  the  general  sensory  continuum 
which  furnishes  the  background  and  setting  for  our  more 
highly   specialized   experiences;    and  on    the   other,   in    the 
warm."  "green."  "hard."  etc.,  we  have  the  attribution  of  a 
special  sensory  quality,  in  this  setting,  to  some  object  ("this") 
singled   out   for   particular   notice.     The   abstraction    which 
singles  out  a  particular  quality  from  the  general  sensory  set- 
ting. Is.  no  doubt.  Intellectual:  it  is  a  mode  of  articulation  or 
organioatlon  of  the  sensory  side  of  experience.    What  remains 
as  the  definitely  sensory  element  Is  (1)  the  unspeclallsed  feel- 
ing of  bodily  existence.     This  is  composed  of  the  memories 
P.ssoo.iation8,   sensations,   etc.,  which   together  constitute   the 
background  of  the  consciousness  of  John  Smith,  as  distinct 
from  that  of  H^nry  Jones,  etc.   We  carry  this  feeling  of  our- 
selves about  with  us:  it  prejudices  us  in  various  ways,  colors 

17 


{lp-=- 


18 


SENSORY  ELKMKNT  IN  JUDGMENT 


all  our  thoughts,  and  spread!  Itself  unnoticed  over  all  our  ex- 
periences. It  Is  more  than  merely  sensory,  but  a  large  part  of 
It  Is  definitely  sensory,  and  requires  consideration,  as  underly- 
ing every  judgment  we  make.  (2)  A  further  sensory  element, 
differing  with  different  judgments,  is  that  by  which  we  dis- 
tinguish "warm"  from  "green, '  etc.,  i.  e.,  not  the  distinguish- 
ing itself,  which  is  i-  ellectual.  but  the  positive  quality  In  each, 
by  which  we  experience  warmth  as  warmth,  as  the  specialised 
mental  reaction  to  a  temperature-stimulus,  and  green  as  green, 
the  specialised  color-consclousneMs,  etc.,  i.  e.,  the  positive 
quality  of  the  special  sensation,  in  virtue  of  which  one  sensa- 
tion can  be  distinguished  from  another.  This  specialised 
sense-experience  is  ultimate,  and  can  not  be  explained  except 
by  reference  to  the  conditions  of  its  appearance  in  conscious- 
ness. It  has  to  be  experienced  to  be  appreciated  as  warmth, 
greenness,  etc.,  and  constitutes  the  specialised  sensory  element 
in  simple  judgments  of  perception. 

(B)     in  Judgments  of  Experience.— What  is  the  sensory  ele- 
ment in  such  judgments  as  "The  freight  trains  crossing  the 
bridge  grow  more  troublesome  every  year"?     What  Is  espe- 
cially present  to  sense  is  ex  hypotheii  no  more  than  a  low 
rumble,  which  is  interpreted  as  due  to  a  distant  freight  train; 
by  association  former  instances  of  such  trains  are  recalled, 
and   a  comparative  judgment,  based  upon   such  experiences 
and  summing  up  their  result,  comes  to  be  formed.    That  is  to 
say,  the  actually  present  sensory  element  is  (1)  the  general 
feeiiug  of  bodily  existence  already  noticed  In  the  case  of  per- 
ceptual judgments,  and  (2)  the  special  coiuplex  of  sense-qual- 
ities which  constitutes  a  "rumble."    So  far  there  Is  not  much 
difference  from  what  we  found  in  the  perceptual  judgment; 
but  In  judgments  of  experience,  the  weight  of  the  judgment 
rests   less   on  the  actually   present   sensory   elements   noted 
above,  and  more  on  the  recalled,  reinstated.  Ideally  present 
sensory  experiences  of  the  past — i.  e.,  less  on  the  present  sen- 
sation, and  more  on  Its  fringe  of  associations.    So  too  of  the 
Inductive  generalisations  of  science,  exemplified  In  such  judg- 
ments as  "All  noise  is  a  compound  of  tones."    This  represents 
a  summing  up  of  past  experiences,  and  the  occasion  for  mak- 
ing such  a  judgment  o!  experience  is,  no  doubt,  some  present 
Instance  of  "noise"  or  "tone."     The  judgment  of  perception 
thus  rests  more  Immediately  on  what  is  present,  the  judg- 
ment of  experience  more  mediately  on  the  given  sensation; 


SYMBOLIC  JUDGMENTS 


19 


but  in  both  cases  the  aensory  element  ronsists  of  (1)  the  gen- 
eral background,  and  (2)  a  apecial  atlmulua  which  aUnda  out 
from  that  background. 

(C)     In  Symbolic  JudsmanU.— In  JudRmentti  auch  as  "Rome 
was  occupied  by  Caeaar."  the  refurente  is,  of  course,  to  an 
experience  into  which   we  do  not  enter   immediately.     We 
reconstruct  for  ourselves  in  idea,  so  far  as  our  own  experience 
furnishes  us  with  analogous  elements,  an  experience  which 
was  never  actually  ours.    What  is  the  sensory  element  In  such 
Judgments?    There  is  certainly  present  (1)  the  actually  given 
senbory  continuum,  the  sense  of  bofMly  existence  which  spreads 
Itself  over  our  reconstructions  and  clothes  the  dry  boces  of 
narrative  with  our  flesh  and  blood,  fusing  the  living  present 
with  a  merely  Imaginary  past,  so  that  we  can  say  Indifrer- 
ently,  either  that  we  are  transported  bodily  into  the  past,  or 
that  the  past  la  made  to  live  aga'.n  in  the  present.    In  addi- 
tion to  this  general  sensory  element,  there  Is  also  present  (2) 
some  special  stimulus  which  directs  our  thoughts  to  the  past, 
to  Rome  for  Instance  rather  than  to  Athens,  and  to  Caesar 
rather  than  to  Pompey.    Such  stimulus  is  furnished  as  a  rule, 
either  by  reading  or  hearing  something  about  Rome  or  Caeaar, 
or  at  least  something  which  by  association  awakens  thoughts 
of  Caesar  and  Rome.     The  special  sensation— c.  g.,  of  visual 
or  auditory  signs  of  worda-Is  here  somewhat  more  remote 
from  the  reconstructed  experience  than  we  found  to  be  the 
case  In  experiential  Judgments,  while  the  general  sensory  set- 
ting seems  to  play  a  relatively  greater  part,  but  In  the  sym- 
bolic judgment  also  the  sensory  element  coualsts  of  (1)  the 
general  background,  and    (2)   some  special  stimulus  arising 
against  that  background. 

(D)  In  Transcendent  Judgments.— In  Judgments  such  as 
"God  is  a  substance  consisting  in  infinite  attributes,"  or 
"Things-ln-themselves  are  absolutely  unknowable,"  i  e  In 
judgments  concerning  entities  which  could  never  be  objects  of 
sense-experience.  It  seems  at  first  sight  as  though  there  could 
be  no  question  of  sensation,  as  though  such  judgments  must 
be  the  product  of  pure  thought,  unmixed  with  any  element 
from  the  sensory  side  of  our  nature.  And  yet,  let  us  consider. 
The  first  Judgment  has  meaning  for  Spinoza's  readers,  pre- 
cisely because  two  of  the  Divine  attributes  are  definitely 
known.  These  are  "extension"  and  "thought."  the  "essence" 
of  body  and  mid,  much  as  we  experience  body  and  mind.    It 


m^ 


20  SENSORY  ELEMENT  IN  JUDGMENT 

is  when  we  extend  the  attributes  of  Deity  so  as  to  include  not 
onWthetlo  which  we  do  experience,  but  also  an  infinity  o 
;S^^r  'oV:hlch';e  are  unable  to  for^  the  sH^^-Udea  th;; 
we  realise  the  transcendent  nature  of  the  i^f^'j'Jl\^l 
a«  we  remain  within  human  experience,  so  far  we  feel  sure 
Tt  our  gr^^ld.  so  far  the  Judgment  has  POBitive  significance 
Jor  us;  the  "infinity"  of  divine  attributes  would  ^^  ""e  J 
meaningless  tor  us  If  we  were  not  a^-^f  -^^7,^,  j",', 
two  of  them,  and  could  thus  regard  the  rc-t  as  a  Rtna  oi 

:ten.ion'Ty  analogy,  of  our  «P-»--'  ^^r  thS^y   t be 
spread  out  this  experience  so  as  to  cover,  ho-   ner  th  nly.  tfie 
ininlte     SO  far   however,  as  the  Judgment     >  «^"-"y  ^^an^ 
ripnt    BO   far  as   It  deals  with  an  Infinity  of  attributes 
:hcrie"carot"ccncelve.  cannot  thin,  l^os^;^-;]^ 
we  are  attempting  to  conceive  the  Inconceivable  and  Judge 
The  unludgea^?e.    In  other  words,  the  transcendent  Judgment, 
^turaland  common  as  It  Is.  really  represents  a  failure  to 
ZZ     imagination  takes  the  place  of  strict  thought,  and 
feenng-^ften.  no  doubt,  sublime,  but  still,  always  merely  sub- 
lectlve— usurps  the  place  of  critical  reason. 
'  ThetTobservatlcns.  however,  do  not  solve  our  present  prob- 
lem    Because  sense-experience  Is  inadequate  to  extend  "sel 
ov^r  the  infinite.  It  does  not  follow  that  the  attemp    is  no* 
actually  made.     In   every   Judgment,  however   transcenden  . 
fhPre  is   in  fact  always  present  (1)  the  general  sensory  set- 
UnTo  folr  X^nll  which  colors  all  our  actual  thinking 
and  projects  Itself  to  distant  spaces  and  times  to  cover  all 
objecteof  our  present  thinking,  such  as  Rome.  Caesar     he 
synaple    God-and  In  virtue  of  so  staging  them  against  the 
sensory  background  of  our  own  experience,  so  colors  them 
Jha    they  become  ours,  parts  of  our  Intimate  self-conscious 
Ixner  ence  here  and  now.    However  inadequate  this  extension 
Z  ^in  t^e  case  of  transcendent,  metaphysical  entitles,  still. 
TLras  we  concern  ourselves  with  them,  we  think  of  them 
?n  insuors  Images.  In  radiations  outward  from  our  presen 
1^0"  Lse-experlence.    Again  (2).  there  Is  always  present 
some  special  sensory  stimulus  which  directs  our  thought  In  o 
TaThs  Which  lead  beyond  the  knowable.  ^^"--^^^^"^^^^^^^^^^^^ 
the  case  of  the  written  or  spoken  symbols  which  furnish  the 
starting-point  for  symbolic  Judgment,  there  Is  no  element  In 
sense^x^rlence  which  Is  unable  to  guide  us  Into  thoughcs 
whlcrdroft.cn  lie  too  deep  for  words.    Our  life  rests  always 


TRANSCENDENT  JUDGMENTS 


21 


upon  a  vast  ocean  of  unsolved  questionings,  and  any  chance 
sensory  stimulus  may  sufBce  to  plunge  us  Into  ti.d  abysses  of 
that  ocean.  Thus  we  see  that  In  transcendent  Judgments  also 
the  sensory  element  consists  of  (1)  the  general  background 
to  which  we  have  so  frequently  referred,  and  (2)  a  special 
stimulus  arising  against  that  background. 

Summary.— If  we  now  cast  our  eyes  over  the  whole  field  of 
judgment,  we  notice  that  while  in  every  case  there  is  present 
a  general  and  a  special  3en8ory  element,  these  are  present  In 
varying  proportions.  As  we  pass  from  perceptual  judgments.  In 
which  the  Intellectual  element  is  relatively  less  Important,  to 
judgments  in  which  the  sensory  element  is  slight  and  the 
intellectual  interpretation  almost  everything,  we  observe  that 
the  general  sensory  background  of  experience  plays  an  Increas- 
ingly greater  part.  On  the  other  hand,  the  special  sensory 
stimulus,  so  vital  in  judgments  of  perception,  becomes  dwarfed 
into  relative  insignificance  In  the  case  of  transcendent  Judg- 
ments. The  stimulus,  e.  g.,  of  a  red  surface,  which  Is  so  all- 
important  for  the  perceptual  Judgment  "This  Is  red,"  Is  of 
importance  for  the  experiential  Judgment  less  as  an  ultimate 
sensory  quality,  and  more  on  account  of  the  associations  which 
it  calls  to  mind.  In  the  symbolic  Judgment,  where  the  asso- 
ciations  are  more  remote,  its  direct  sensory  quality  is  still  less 
important,  and  finally,  in  the  transcendent  Judgment,  It  Is 
almost  a  chance  affair,  almost  a  matter  of  Indifference:  for  all 
roads  lead  alike  to  the  obstinate  questionings  which  underlie 
and  perplex  our  whole  life.  Great,  however,  as  are  these 
variations,  in  every  Judgment  we  find  present  both  general 
and  special  elements  of  a  sensory  kind. 

FOE  FURTHER  READING 

\V.  James,  Principles  of  Psychology,  Vol.  II,  chapter  xvU.  H.  Lotie, 
Logic,  sect.  2.  A.  Riehl,  Der  philosopMsche  Kriticismus,  Vol.  II, 
chapter  1.  G.  F.  Stout,  Manual  of  Psychology,  Bk.  II,  chapters  Mi. 
Proceeding!!  of  the  Aristotelian  Bociety,  N.  S.,  Vol.  VI,  pp.  860-362 
(quoted  In  B.  Gibson,  The  Problem  of  Logic,  pp.  82-84).  W.  Wundt 
Logik,  (.Ird  Edit.),  Vol.  I,  pp.  10-60. 


EXERCISES 

t.  What  precisely  are  the  sensory  elements  In :  Here  comes  Mr. 
Smith.    This  bread  tastes  excellent.    I  am  taller  than  you? 

2.  What  precisely  are  the  sensory  elements  In :  Electricity  Is  moch 
more  efficient  than  gas.     Such  requests  for  subscriptions  always  sue- 


22 


SENSORY  ELEMENT  IN  JUDGMENT 


ceed.     Bggs  placed   In   water-glass   keep  for  several   months.     I  am 
always  nervoua  before  a  large  audience?  „  ,      „      ♦u.„ 

3  W-hat  predsely  are  the  sensory  elements  In :  Not  more  than 
three  men  In  a  thousand  would  vote  for  that  program  At  least  fifty 
per  cent  of  actions  called  criminal  are  due  to  our  social  syatem.  For 
a  small  house,  you  will  find  hot  water  heatlr,     the  most  satisfactory  ? 

4  What  precisely  are  the  sensory  elements  In:  God  moves  in  a 
mysterious  way,  Ills  wonders  to  perform.  Time  and  space  are  unreal 
forms  of  sense,  and  dlsguUe  the  Real.  I  want  to  be  a  great  Arttat. 
I  listened  to  the  Unguage  of  the  birds ;  I  knew  what  the  trees  whisper 

5  Read  Henry  James:  The  Soft  Side,  pp.  8-9.  18-21.  and  sum- 
marls*   the  essential  nature  of  sensory  experience,  as  there  described. 


CHAPTER  III 

VALIDITY  AND  THE  SENSORY  ELEMENT. 

The  Question  Concerning  Validity.— In  the  last  chapter  we 
have  described  the  sensory  element.    We  have  treated  It  as  a 
fact,  as  a  constituent  part  of  every  judgment,  and  have  stated 
what  It  la,  what  we  find  it  to  be.    All  this,  however,  Is  merely 
preliminary  to  a  further  question,  which  is  the  essential  ques- 
tion for  logic.     It  remains  to  ask,  not  what  the  fact  is,  but 
—what  Is  the  value  of  the  fact?    Being  what  we  have  found  it 
to  be,  does  this  universally  present  sensory  element  in  any 
way  Contribute  to  the  validity  of  judgment?    Do  the  correct- 
ness, certainty,  reliability,  truth  of  the  perception  of  warmth, 
redness,  etc.,  depend  on  our  bodily  senses?    Are  we  to  regard 
sense-perception,  the  sensory  element  in  judgment,  as  trust- 
worthy per  se,  or  as  untrustworthy — or  is  it  possibly  indif- 
ferent?   Is  our  s     -1  of  warmth,  for  example,  perhaps  merely 
a  de  facto  condltl     .  a  transient  event  in  our  embodied  expe- 
rience without  which  we  should  not  judge  a  given  object  to 
be  warm — a  mere  happening  and  nothing  more — ^and  do  we 
have  to  look  elsewh'ive  for  de  jure  conditions,  criteria  which 
really  test  the  cor    ctness  and  trustworthiness  of  the  judg- 
ment?!   Are  truth  and  certainty  entirely  an  affair  of  "intel- 
lect," or  do  our  bodily  senses  themselves  contribute  something 
by    which    the    validity    of    judgments    can    be    tested    and 
approved? 

(A)  In  Judgments  of  Perception. — In  judgments  such  as 
"This  room  is  warm,"  there  is  no  doubt  that  our  bodily  senses 
play  a  great  part.  But  the  present  enquiry  is  whether  this 
part  which  they  play  is  altogether  reliable  and  trustworthy — 
more  particularly,  whether  any  attempt  to  justify  such  judg- 
ments inevitably  ends  In  an  appeal  to  sensory  experience  as 
such.  Let  us  consider.  Suppose  I  feel  doubtful  as  to  whether 
the  room  is  warm  after  all.  I  can  either  (1)  repeat  my  Judg- 
ment, i.  e.,  give  myself  up  to  the  sensory  feeling,  and  assure 


1  Cf.  Wundt,  Logik.  Vol.  1,  i».  80. 


23 


24         VALIDITY  AND  THE  SENSORY  ELEMENT 

myaelf,  by  yielding  completely  to  Its  guidance,  that  the  room 
certainly  does  feel  warm,  or  at  least  feels  warm  to  me.    This, 
In  fact,  is  our   usual  proceci.   e  in  testing  perceptual  Judg- 
ments    That  Is  to  say,  we  accept  as  trustworthy  the  sensory 
elevn         as   such,   and   only   doubt   whether   we   really   had 
allo'    a  it  full  play,  or  whether  we  perhaps  were  inattentive 
on  the  previous  occasion,    'f  ♦he  second  experiment  confirms 
the  first  judgment,  we  ar  r  up?^aily  ..atisfied,  and  enquire  no 
further.    If,  however,  our  judgment  is  challenged  by  someone 
else,  or  if  we  have  reason  to  suspect  that  perhaps  our  senses 
are  deranged,  as  by  a  fever,— in  which  case  we  may  feel  warm, 
although  the  temperature  of  the  room  may,  in  fact,  be  low- 
in  such  cases  we  usually  appeal  to  a  thermometer,  or  some 
similar  objective  measure,  which  represents  changes  of  tem- 
perature in  a  way  that  appeals,  at  least  immediately,  to  some 
sense  other  than  that  of  warmth,  e.  g.,  to  the  eye.    This  also, 
we  must  notice,  is  an  appeal  to  sense-experience,  and  in  actual 
fact,  if  hard  pressed,  we  are  driven  to  the  conclusion  that, 
whatever  the  thermometer  may  or  may  not  state,  whatever 
the  temperature  of  the  room  may  or  may  not  be,  we  feel  warm. 
We  feel  what  we  feel,  and  cannot  be  argued  out  of  our  feeling 
by  any  reasonings  drawn  from  the  reading  on  the  thermom- 
eter, etc.    It  is  a  matter  of  sensory  feeling,  and  not  of  rea- 
soning.    In  other  words,  our  conclusion  is,  that  the  sensory 
element  in  the  Judgment  is  our  own  feeling  of  warmth,  and 
if  our  judgment  that  the  room  is  warm  turns  out  to  be  false, 
the  falsity  depends  not  on  the  sensory  element,  which  is  what 
it  is  independently  of  reasonings  about  it,  but  on  the  intel- 
lectual element  which,  given  the  feeling  of  warmth,  interprets 
this  experience  as  due  to  the  temperature  of  the  room.    The 
same  is  the  case  with  all  the  "illusions  of  sense"  produced  by 
mirrors,  prisms,  or  cunningly  devised  appeals  to  misleading 
associations.    The  error  depends  in  all  such  cases  upon  some 
misinterpretation  which  leads  us  away  from  the  direct  appre- 
hension of  the  sensory  elements.     Where  we  are  not  so  led 
astray,  where  we  directly  apprehend  those  elements,  the  sim- 
ple sensory  experiences  are,  as  we  have  seen,  "ultimate."    In 
perceptual  Judgments,  all  that  we  can  do  to  test  their  validity 
is,  avoiding  interpretations  and  associations  as  far  as  possi- 
ble, to  analyse  the  given  case  and  break  it  up  into  parts  so 
simple,  that  an  unbiased  appeal  to  sensory  apprehension  can 
be  made,  and  then— trust  absolutely  to  our  direct  apprehen- 


IN  EXPERIENTIAL  JUDGMENTS 


2S 


slon  of  the  sensory  elements.  Direct,  simple,  sensory  appre- 
hension thus  furnishes  the  ultimate  basis  for  testing  and 
approving  the  validity  of  judgments  of  perception. 

(B)     In  Judgments  of  Experience.— In  perceptual  Judgments 
it  Is,  after  all,  not  difficult  to  see  that  the  sensory  element 
must  condition  the  validity  of  our  thinking.    We  have  merely 
to  free  ourselves  from  misleading  Interpretations  and  asso- 
ciations, and  make  an  unbiased  sensory  Judgment.     But  In 
judgments  of  experience  the  element  of  interpretation  seems 
more  essential.    Such  judgments  represent  a  summing  up  of 
sensory  experiences,  and  the  associations  are  vital  to  the  con- 
clusion.   Here,  at  any  rate,  there  can  be  no  question  of  "free- 
ing ourselves  from  Interpretations  and  associations";  for  this 
would  be  to  deprive  us  of  the  experiential  Judgment  altogether. 
When,  for  instance,  on  the  sensory  basis  of  a  low  rumble,  I 
interpret  my  experience  as  due  to  a  freight  train  crossing  the 
bridge,  surely  the  case  is  parallel  to  the  interpretation  of  a 
feeling  of  warmth  as  due  to  the  temperature  of  the  room;  and 
when  I  further  compare  the  disturbance  due  to  freight  trains 
in  recent  years  with  the  similar  experiences  of  the  past,  my 
judgment  Is  surely  based,  at  least  In  large  part,  on  associa- 
tions rather  than  directly  apprehended  sensations.    Judgments 
of  experience  are  thus  more  complex,  and  seem  to  require  a 
different  kind  of  explanation.     And  yet,  if  we  wish  to  dis- 
cover whether  the  sensory  element  here  also  is  a  conditioning 
factor  In  determining  the  validity  of  the  Judgments  in  ques- 
tion, we  must  ask,  precisely  as  we  did  before,  whether  the 
attempt  to  justify  such  Judgments  inevitably  ends  in  an  appeal 
to  sensory  experience. 

Let  us  consider.  If  such  a  judgment  were  challenged,  how 
should  we  attempt  to  justify  it?  If  it  were  doubted,  for 
instance,  whether  the  rumble  was  really  due  to  a  train,  we 
should  Justify  our  statement  by  leading  the  doubter  to  the  rail- 
way bridge,  and  letting  him  see  as  well  as  hear  the  train.  We 
should  then  withdraw  him  gradually  from  the  bridge,  until  he 
sufBciently  realised  that  the  roar  of  the  train  gradually 
changed  Into  the  low  rumble  In  proportion  as  he  drew  further 
away  from  the  bridge.  This  gradual  transition  would  assure 
him  of  the  continuity  of  the  sensory  experience,  and  he  would 
come  to  see  that  what  in  the  distance  was  a  rumble  was  in 
fact  one  with  what  was  experienced  as  a  "roar  of  the  train" 
in  the  neighborhood  of  the  bridge.    In  other  words,  the  proof 


26         VALIDITY  AND  THE  SENSORY  ELEMENT 


of  the  validity  of  our  judgment  consists  in  an  appeal  to  actual 
sensory  experience.  In  this  proof  we  show  that  the  rumble 
sensation  if  continuous  with,  and  in  fact  is,  the  sense-percep- 
tion of  a  dlstant-train-crossing-brldge.  The  Intellectual  ele- 
ment consists  chiefly  in  so  ordering  the  experience  that  the 
doubter  could  give  himself  up  to  the  sensory  side  of  the  expe- 
rience, and  realise  for  himself  its  thorough-going  continuity. 
This  appeal  to  unbiased  sensory  experience  is  accepted  as  final. 

"Yes,"  it  might  be  objected,  "but  this  is,  after  all,  a  per- 
ceptual judgment.  You  have  an  auditory  perception  of  a  dis- 
tant train.  This  is  a  little  more  elaborate  than  the  percep- 
tion of  bodily  warmth,  but  in  the  last  analysis  is  much  the 
same  kind  of  judgment,  and  in  such  judgments  we  have  already 
granted  that  the  ultimate  appeal  is  to  sense-experience.  But 
how  about  a  judgment  in  which  the  reference  is  not  to  pre- 
sent perception,  but  to  the  distant  past?  How  could  we  justify 
such  a  thought  as  that  the  freight  trains  in  recent  years  are, 
on  the  whole,  more  troublesome  than  the  freight  trains  in  the 
remoter  past?"  —Well,  we  answer,  how  do  we  justify  such 
judgments?  The  usual  method  Is  to  appeal  to  the  memory  of 
a  number  of  the  local  inhabitants  who  have  experienced  the 
disturbance  in  question  during  a  suflicient  period  of  years. 
If  their  conclusions  agree  with  ours,  reasonable  doubt  is 
usually  satisfied.  In  what,  then,  does  this  justification  by 
appeal  to  memory  consist?  It  is  necessary  to  Inquire,  for  the 
appeal  to  memory  is  certainly  an  appeal  to  associations,  and 
associations,  as  we  have  already  seen,  are  not  always  to  be 
trusted.  What,  then,  constitutes  the  essential  difference 
between  a  trustworthy  recollection,  and  an  association  which 
we  cannot  trust? 

Let  us  compare  the  former  case — in  which  uncertainty  as 
to  the  distant  train  is  removed  by  our  realising  the  spatial 
continuity  of  (1)  the  rumble  and  (2)  the  train-actually-seen- 
on-the-bridge.  In  that  case,  the  validity  of  our  judgment 
rested  on  the  spatial  continuity  of  our  sensory  experience;  the 
experience  of  the  "rumble"  actually  was  an  experience  of  the 
spatially  distant  train.  In  the  present  case,  can  we  show  that 
the  rumble-experience  is  actually  an  experience  of  trains  dis- 
tant In  time  rather  than  in  space?  In  other  words,  does  our 
sensory  experience  possess  not  merely  spatial,  but  also  tem- 
poral continuity?  Let  us  examine  this.  The  actual  sensory 
present,  according  to  psychologists,  embraces  a  period  of  time 


tot'/r  ■  :■ 


r<  t^  tiA.y,^l 


hj^ 


1/ 


IN  EXPERIENTIAL  JUDGMENTS 


27 


covering  approximately  from  two  to  four  seconda.    Our  sen - 

sory  conaclousnesd  Is  at  Its  best  at  this  brightly  Illuminated 
focal  point,  and  It  is  what  Is  brought  Into  the  center  of  focus 
that  we  apprehend  most  clearly.    But  our ''sensory  conscious-  — ~ 
ness  has  also  a  margin,  and  from  the  brightness  of  the  focal 
center  to  the  darkness  of  the  extreme  margin  there  Is  unbroken 
continuity,  a  twilight  which  deepens  by  Imperceptible  grada- 
tions.    So   It  Is  with  memory,  with  our  associations.     The 
nearer  they  are  to  the  present,  the  more  closely  connected  with 
the  focus  of  sensory  experience,  the  more  clearly  can  we  appre- 
hend their  value.    They  are  always  continuous,  in  the  stream 
of  consciousness,  with  present  sensation.    What  makes  us  trust 
the  memories  of  yesterday,  and   mistrust  the  memories  of 
many  years  ago,  is  not  absence  of  continuity,  but  some  diffi- 
culty In  so  ordering  our  mental  vision  that  we  can  directly 
apprehend  that  continuity.    Where  we  leap  to  conclusions  with- 
out establishing  that  direct  apprehension,  we  have  untrust- 
worthy, uncritically  accepted,  associations.     In  order  to  test 
critically  the  trustworthiness  of  memory,  we  experiment  with 
our  associations   until   we   are   In   a  position   to  apprehend 
directly,  without  bias,  and  in  the  present,  some  sensory  ele- 
ment which  extends  with  clearly  unbroken  continuity  into 
the  past.     In   such   cases,   just   as   the    rumble-sensation   Is 
directly  continuous  with  the  spatially  distant  train-roar  of 
two  seconds  ago,  so  also  It  Is  directly  continuous  with  the  tem- 
porally distant  train-roar  of  ten  years  ago.    In  other  words, 
the  justification,  in  both  cases,  depends  on  establishing  clearly 
the  continuity  of  the  sensory  experience  In  space  and  time, 
in  such  a  way  that  we  directly  apprehend  the  distant  (whether 
in  space  or  In  time)  as  an  extension,  towards  the  margin,  of 
the  present  focal  sensory  consciousness. 

Finally,  In  the  case  of  the  Inductive  generalisations  of 
empirical  science,  such  as  "All  noise  is  a  compound  of  tones," 
justification— or,  as  It  Is  termed  In  science,  "verification"— 
consists  In  an  appeal  to  "demonstration,"  i.  e.,  to  the  direct 
sensory  experience  of  a  typical  case.  Thus  we  see  that  the 
judgment  of  experience  is  merely  a  complex  and  elaborate 
case  of  the  Judgment  of  perception,  and,  like  the  perceptual 
judgments  examined  previously.  Is  dependent,  for  Its  validity, 
upon  a  direct  apprehension  of  the  sensory  element.  The  asso- 
ciations which  are  misleading,  and  the  interpretations  which 
withdraw  our  attention  from  this  sensory  apprehension,  must 


28 


VALIDITY  AND  THE  SENSORY  ELEMENT 


first  be  removed;  we  can  then  realise  the  full  force  of  the 
sensory  elements,  with  their  spatial  and  temporal  continuity, 
and  see  how  they  underlie  and  make  verifiable  the  Judgments 
of  experience. 

(C)     In  Symbolic  Judgments. — Baaed  as  it  is  on  direct  past 
experience,  it  is  fairly  Intelligible  that  the  experiential  Judg- 
ment can  be  verified     i  an  extended  perception,  which  fuses 
together  past  and  present  in  a  living  unl*y.    It  is  in  fact  an 
extended   perceptual  Judgment.     But  when  we   come  to   the 
symbolic  Judgment,  a  striking  difference  seems  to  confront  us. 
In  the  symbolic  Judgment  we  attempt  to  reconstruct,  not  a 
distant  experience  of  our  own,  but— an  experience  which  was 
never  ours,  an  experience  which  may  have  belonged  to  some- 
one else  in  the  past,  or  may  some  day  come  to  us— or  to  some- 
one else— in  the  future.    Surely  in  such  cases  there  can  be  no 
question  of  extending  some  ray  of  focal  Illumination  into  the 
marginal  twilight  of  our  own  consciousness — surely  here  there 
can  be  no  resting  upon  the  living  continuity  of  our  own  sen- 
sory  experience.     In  studying,   for  Instance,  the   history  of 
Rome,  we  note  its  occupation  by  Caesar.    Except  metaphoric- 
ally, we  cannot,  of  course,  transport  ourselves  Into  the  first 
century  before  Christ,  and  consequently  there  can  be  no  ques- 
tion  of   "apprehending   directly   one   continuous   experience" 
which  extends  back  to  the  occupation  of  Rome  in  one  complex 
perceptual   Judgment.     It   would    seem,   then,   that   symbolic 
judgments  require  a  different  kind  of  explanation,  a  different 
kind  of  answer  to  the  question  which,  here  again,  we  must 
ask:— In  attempting  to  Justify  such  Judgments,  do  we  inevit- 
ably appeal,  in  the  end,  to  sensory  experience? 

It  must  at  once  be  admitted  that  no  personal  experience  can 
possibly  assure  us  of  the  certainty  and  truth  of  eve"ts  which 
He  beyond  that  experience.  What  Caesar  did  when  he  entered 
Rome,  we  do  not  exactly  know;  as  we  should  say,  we  were 
not  there  to  see.  Accordingly  we  have  to  trust  to  tradition 
rather  than  to  personal  experience,  and  to  Indirect,  In  place 
of  direct,  evidence.  Furthermore,  familiarity  with  the  errors 
of  history  books,  as  well  as  with  works  of  professed  fiction, 
will  convince  us  that  we  can  not  Infer  with  certainty  from  the 
printed  statement  to  the  actual  occurrence  of  events.  The 
certainty  and  truth,  then,  of  symbolic  Judgments  Is  and  must 
be,  in  the  nature  of  the  case,  largely  a  matter  of  Interpreiu- 
tlon.  of  intellectual  rather  than  sensory  elements.     In  this 


IN  SYMBOLIC  JUDGMENTS 


29 


reapett,  symbolic  Judgmenta  resemble  the  perceptual  Judg- 
ment -It  is  warm  in  the  room";  i.  e.,  the  immediate  sensory 
element  is  something  less  than  the  total  Judgment,  to  which 
intellectual  elements  also  have  contributed  their  part.    As  in 
the  perceptual  Judgment,  in  examining  into  its  validity  we 
abstracted  from  Intellectual  elements,  and  laid  bare  the  sen- 
sory element  in  order  to  apprehend  it  dlrecUy  in  its  full  force, 
80  here  In  the  symbolic  Judgment,  let  us,  for  the  present,  leave 
out  of  consideration  the  Intellectual,  Interpretative  element, 
and  try  to  discover  what  the  sensory  element  is,  and  what 
part  It  plays  in  the  something  less  than  the  total  Judgments 
If,  then,  we  leave  out  of  consideration  the  question  as  to 
whether,  in  actual  fact,  Caesar  did  or  did  not  occupy  Rome 
in  the  manner  indicated  by  our  history  book,  what  remains  of 
the  complex  Judgment?     There  remain  two  parts  which  we 
still  think:— (1)  we  still  think  that  the  history  book  states 
that  Rome  was  occupied  by  Caesar;  (2)  we  still  try  to  experi- 
ence, as  well  as  we  can,  the  wider  meaning  of  this  statement, 
».  e.,  what  a  Roman  citizen  must  have  felt,  how  Caesar  him- 
self must  have  felt,  etc.    In  the  first  case,  if  our  Judgment  is 
challenged— suppose  it  maintained,  e.  g.,  that  we  have  mis- 
read the  book,  that  there  is  no  literary  evidence  for  Caesar's 
having  occupied   Rome— in   such  a  case,  the  only  possible 
appeal   is  to  direct  sensory  experience  of  the  printed  page 
The  doubter  must  read  for  himself,  and  have  direct  sensory 
experience  of  the  printed  symbols,  in  order  to  reconstruct  for 
himself  their  meaning.    The  final  appeal  is  certainly  here  to 
the  sensory  element  in  experience,  and  the  thought  appears  to 
be  a  complex  perceptual  Judgment.     "The  book  has  black 
marks  in  it"  is  obviously  a  Judgment  of  perception.     If  the 
black  marks  are  regarded  as  symbols,  "The  book  contains 
symbols"  is  still  a  perceptual  Judgment.     So  too  with  the 
thought  that  the  book  contains  letters,  words.  English  words, 
the  definite  English  words  "Rome"  "Was"  "Occupied"  "By"' 
"Caesar."    In  short,  the  Judgment  "The  book  states  that  Rome 
was  occupied  by  Caesar"  is  a  complex  perceptual  Judgment,  a 
legitimate  extension  of  the  direct  sensory  apprehension  of  the 
letters  in  the  book.    Or  if  it  is  the  associations  that  we  empha- 
sise, by  means  of  which  we  are  able  to  read  printed  symbols.  ' 

i^.i'*^Y''**J°.*. '*''**''y  "•^'^  '»  '•*««  than  the  total  Judrment  la  eanin 
lent  to  what,  In  a  work  of  flctVon,  U  the  entire  ludSSInt-i  «  ^iIUL" 
no  clahn  to  reprMent  the  external  conT^  of  i^rtuSf^StTu;  SidJ^ 


30 


VALIDITY  AND  THE  SENSORY  ELEMENT 


in  that  rase  we  have  a  Judgment  of  experience.  In  both  cases, 
however,  the  appeal  is  certainly  to  direct  sensory  apprehen- 
sion, and  that  is  the  final  sensory  evidence  for  the  validity  of 
our  Judgment. 

The  second  part  of  our  Judgment  is  an  extension  of  the 
meaning  which  we  apprehend  in  reading  the  book.  If  asked 
with  what  right  we  build  up  some  approximation  to  the  expe- 
rience of  Caesar  and  the  Roman  citizens,  we  can  only  state 
that  it  is  a  legitimate  extension  of  the  meaning  of  what  we 
have  before  us.  As  we  read  the  printed  symbols,  the  sensory 
experience  of  the  meaning  of  the  words  "Rome,"  "Occupied 
by,"  "Caesar,"  etc.,  expands  so  as  to  include  appropriate  ele- 
ments from  our  own  experience  In  one  continuous  whole,  so 
that,  so  far  as  this  personal  experience  permits,  our  reading 
is  no  neutral  exercise  in  spelling,  but  is  a  fuller,  richer,  more 
adequate  experience  which  approximates  to  the  actual  life 
about  which  we  are  reading.  We  cannot  feel  the  actual  glow 
of  triumph  which  animated  Caesar's  veterans,  or  the  confu- 
sion and  blind  panic  of  the  partisans  of  Pompey.  We  do  not 
know  the  Italian  sky,  the  Roman  crowds.  But  we  have  all  had 
some  experience  of  triumph,  or  panic;  we  have  all  experienced 
warm  suns,  blue  skies,  Jostling  crowds.  And  out  of  such  expe- 
riences we  can  piece  together  something  which  comes  to  us 
with  the  warmth  and  Intimacy  of  personal  experience,  and  at 
the  same  time  represents  for  us,  by  analogy,  a  pale  copy  of 
the  experlencps  symbolised,  the  Roman  scenes  about  which  we 
are  reading  The  validity  of  this  reconstruction  rests  wholly 
upon  the  meaning  of  the  documentary  evidence  before  us. 
We  must  abstract  from  misleading  associations  and  uncritical 
interpretations,  and  confine  ourselves  to  legitimate  expansion 
—the  extension  authorised  by  what  we  read.  In  other  words, 
the  validity  of  the  symbolic  Judgment  rests  on  the  same  evi- 
dence as  the  experiential  Judgment;  as  far  as  It  goes,  it  is  to 
the  sensory  element  that  we  must  at  last  appeal,  as  the  touch- 
stone of  Its  validity. 

(D)  in  Transcendent  Judgments.— Transcendent  JudRments 
represent,  in  extreme  form,  an  element  which  has  been  grad- 
.  ually  forcing  Itself  upon  our  attention  In  the  preceding  cases. 
In  the  Inductive  generalisations  of  empirical  science,  i.  e.,  In 
judgments  of  experience,  the  utmost  we  can  do  is  to  approxi- 
mate to  certain  knowledge.  There  is  always  some  slight  gap 
between  the  law  we  wish  to  establish,  and  the  evidence  on 


/ 


IN  TRANSCENDENT  JUDGMENTS  31 

which  It  TeutB.  Inductive  evidence  can  come  as  close  to  com- 
plete proof  as  we  please;  but  there  Is  always  wme  falling 
«hort^  some  Inability  to  esUbllsh  perfect  certainty.  In  Je 
symbolic  Judgment,  this  gap  is  still  more  noticeable.  Reor- 
ganise and  reconstruct  our  personal  experience  as  we  may 
we  can  never  quite  enter  Into  '.e  experiences  of  others,  or' 
nto  experiences  which  have  never  yet  been  ours.     Anai;g^' 

in  d'iim""'!  '"'■""'  'd«°tlty-but  we  always  fall  short^ 
full  Identity,  always  fall  to  pass  completely  the  gulf  which 
separates  desire  from  performance.  In  other  words,  our  actual^ 
experience  always  falls  short  of  the  ideal  which,  all  uncon- 
sciously drives  us  onward,  and  is  the  hidden  root  of  that 
d issatisfact  on  with  the  not-quite-perfect.  which  fastens  upon  ' 
all  of  us  at  times,     m  the  transcendent  judgment,  this  Idea" 

s  more  Insistent,  and  the  gap  between  whit  wTactuaHy  a«a,„ 
and  the  perfection,  the  consummation  of  Infinite  desire,  Is  at 
Us  greatest.    We  can  never  know  Thlngs-In-themselves!  never 

ZiT""  /'!   rr  '^'"'^'   ''«  "°''-''''°«  Substan;e    'he 
Divine,  perfect.  Infinite  experience  In  which  all  the  Illusions 

?r„ np'''^  T'''.  °'  °"  '*°'*''  *"""»y  '^^^^'^^  efforts  are 
transcended  and  made  perfect  in  harmony,     if  empirical  and 

symbolic  judgments  cannot  be  completely  verified,  how  much 

more  Is  this  the  case  with  transcendent  judgments!     ItTsof 

L  dZu  ^'''''Jir'  ^^°°'  '^«  '•«*''"  °'  experience,  of 
ence.  but  are  constructed  by  idealising  Intelligence.  "Things-  - 
in-themselves"  mean  things  beyond  that  aspect  which  alone 
we  experience;  "God"  Is  Infinitely  greater  than  the  Ideas  we 
can  form  of  Him;  the  "Vision  Splendid"  which  guides  our 
efforts  towards  a  better,  finer  life.  Is  broader,  deeper  subllmer 
than  anything  we  have  known.  How  then  can  we.  In  the  ore^ 
ent  case,  ask  whether  the  validity  of  such  Judgments  depends 
on  the  sensory  element  in  our  thought' 

The  case  Is.  perhaps,  not  as  hopeless  as  It  appears.  Tran- 
scendent judgments,  as  we  have  already  seen.  «,ntaln  some 
sensory  elements.  The  metaphysical  concept  of  God  does  not 
s  and  out  Of  all  relation  to  human  life:  the  sphere  ofldea 
Divinity,  though  larger  than  mere  humanity.  Includes  all  our 
experiences  as  a  portion  of  Itself;  the  finite  is  not  only  tranl 
scended  by.  but  Is  contained  In,  the  Infinite.     All  Ideals    it 

connection  with  our  sensory  experiences.    Let  ua  consider  aj 


32        VALIDITY  AND  THE  SENSORY  ELEMENT 

concrete  case,  for  Instance,  the  ideal  of  personality.  We  form 
our  concept  by  putting  together  appropriatf>  jxperienres  of 
our  own,  and  then  transcending  them  In  the  direction  of  a 
more  inclusive,  or  rather  an  o/MnclusIre  concept.  We  can 
take,  for  example,  the  personality  of  the  grammar-school  grad- 
uate, of  the  high-school  graduate,  of  the  university  graduate, 
and  link  them  up  with  our  present  focal  consciousness  in  a 
curve  representing  the  development  in  personality,  somewhat 
thus:  — 


So  far,  we  have  a  judgment  of  experience,  a  complex  sum- 
ming up  of  many  perceptions.  But  we  can  go  a  little  fur- 
ther; we  can  produce  the  line  of  the  curve  a  little  beyond  the 
point  we  have  actually  reached;  we  can  look  ahead,  and  so 
far   as   we    remain   within    reasonable   limits,   we    transcend 


r-^, 


f<7-'J*«( 


H,     f  ^^v  fJL/i,.,^ 


A/^ 


•t^V*" 


IN  TRANSCENDENT  JUDGMENTS  « 

wnicn  we  thus  form  is  JuBtlHed  procixelv  an  r.r  ..  if  -1/ 

dire.!  .ppr.l,e„.,„„  „,  Jh.  ,el™  eSj^  ZrT*^  '°''   ' 


34 


VALIDITY  AND  THE  SENSORY  ELEMENT 


vlouB  chapter  we  saw  that.  In  passing  from  the  simpler  to 
the  more  complex  types  of  judgment,  the  Intellectual  element 
plays  a  greater  part,  while  the  sensory  element  plays  at  any 
rate  a  less  direct  part.  We  saw  further  that  the  direct  sen- 
sory stimulus  plays  a  greater  part  in  the  simpler  judgments, 
while  in  the  symbolic  and  transcendent  types  the  stimulus  is 
relatively  overshadowed  by  elements  from  the  sensory  back- 
ground. In  the  present  chapter  we  have  deliberately  neg- 
lected, so  far  as  possible,  the  intellectual  element.  We  have 
noted  in  passing  that  to  judge,  on  the  basis  of  a  warmth-sen- 
sation, that  ''The  room  is  warm"  requires  Intellectual  elements, 
and  that  in  experiential,  symbolic,  and  transcendent  judg- 
ments the  gulf  between  direct  sensation  and  full  judgment  has 
grown  increasingly  wider,  t.  e.,  that  the  intellectual  element 
has  played  an  increasingly  greater  part.  But  leaving  to  sub- 
sequent chapters  all  consideration  of  the  part  played  by  intel- 
ligence, we  have  conflned  ourselves  to  studying  the  impor- 
tance, for  the  validity  of  the  judgment,  of  the  directly  appre- 
hended sensory  elements. 

In  estimating  the  validity  of  a  perceptual  judgment,  which 
asserts  the  warmth,  heaviness,  redness,  etc.,  of  an  object — i.  c, 
which  deals  in  sense-qualities — it  is  impossible  to  test  its  accu- 
racy without  appealing  to  sense-perception,  in  which  alone 
such  qualities  can  be  directly  and  satisfactorily  experienced. 
Similarly  in  judgments  of  a  more  complex  type,  so  far  as 
these  are  based  upon  sensory  experiences,  any  test  of  validity 
must,  in  the  end,  appeal  to  direct  sense-experience;  for  com- 
plete satisfaction  of  the  desire  for  validity  we  must  be  able 
to  apprehend  in  one  continuous  connection  the  sensory  expan- 
sion from  the  stimulus  which  includes  the  relevant  elements 
drawn  from  the  general  sensory  background  of  experience. 
The  same  is  true  of  symbolic  and  transcendent  judgments;  so 
far  as  these  contain  sensory  elements,  we  can  pass  upon  their 
validity  only  so  far  as  we  come  to  apprehend  clearly  and  with- 
out bias  iheir  continuous  connection  with  the  focus  of  sensory 
consciousness.  So  far  as  symbolic  and  transcendent  judgments 
really  follow  without  deviation  the  directions  approved  by  the 
judgments  of  experience — i.  e.,  so  far  as  these  extensions  of 
the  focal  consciousness  are  governed  strictly  by  elements  ver- 
ifiable In  sense-experience,  so  far  they  are  valid.  So  far  as, 
without  violating  this  condition,  they  transcend  sensory  vert- 


CONCLUSION 


35 


flablllty.  they  may  or  may  not,  perhaps,  be  valid,  but  such  a 
point  cannot  bt,  rieclded  by  an  appeal  to  sensory  experience. 

To  sum  up:— gsjrar  as  Judgment  contaln^^etwory  elemanta^ 
our  thought  depends  on  jensory  ^aPDreliepsion,  and  so  far  as 
the  sensory  apprehension  to  which  we  appeal  is  valid,  so  far 
the  Judgment,  at  least  on  Its  sensory  side.  Is  valid.     In  its 
simplest  and  most  direct  forms,  sensory  apprehension  Is  ulti- 
mate  and   its  validity  beyond   reasonable   question.     Conse- 
quently, so  far  as  the  sensory  element  in  Judgment  can  be 
reduced  to  these  simplest  and  most  direct  forms  of  sensory 
apprehension,  or  to  som.  legitimate  and  continuous  extension 
of  these.s  so  far  the  Judgment  itself,  on  Its  sensory  side,  is 
valid.    In  other  words,  so  far  as  Judgment  contains  sensory 
elements.  Its  validity  depends  wholly  upon  direct  appreuen- 
slon  of  those  sensory  elements.    So  far  as  it  contains  elements 
other  than  sensory,  nothing  has  been  as  yet  determined  as 
to  its  validity,  though  a  suspicion  has  been  expressed  that  the 
validity  of  other  elements  also  will  be  found,  in  the  end,  to  be 
verifiable  only  by  reference  to  sense-experience.    The  consid- 
eration,   however,    of    such    non-sensory    elements   must   be 
deferred  to  the  succeeding  chapters. 

jnven   *"«   jts   extension    .  are    contlnnons    with    each    othftr 


FOR  FURTHER  READINO 

"oJ.f  *^^'  ^''''^'  ***^*-  267,  pp.  837-.'»a9.    Chr.  Slywart.  Loaic  Vol    I 
pp.  262-264.     W.  Wundt.  Logtk,  (3rd  Edit ).  Vol    I    pp  VHs^'  ' 

BXBRCISBS 

fho  fnlfii  ""^^^^J^  **  '^'^^  **  sense-experience  In  order  to  Justify 

,J'fr.u!l  necessary  to  appeal  to  sense-experlence  In  order  to  Justify 
^eaJn'rs^pteX;^"^"^-     ^"^^^  O--'^-  thirst.     Peaches  L  In' 

■  ,^fW  ^Iv"  °«'"^«'*'"y  to  appeal  to  sensory  experience  In  order  to 
.'hnf  u  .  ^"?'"*''nK  =  This  studeat  has  been  below  grade  so  often 
that  It  I,  mathematically  Impossible  for  him  to  reach  a  passing  ^.de 


36 


VALIDITY  AND  THE  SENSORY  ELEMENT 


this  term.     Nothing  ventare,  nothing  win.     It'«  sure  to  be  cold  in 
January? 

4.  Is  It  necesMiry  to  appeal  to  sense-experience  In  order  to  Justify 
the  following :  It  Is  impossible  for  a  thing  both  to  be  and  not  to  be. 
Bm  niMlo,  nihil  fit.    The  soul  is  a  simple,  uncompounded  substance? 

5.  Do  novelists  find  It  necessary  to  appeal  to  sensory  experience, 
even  when  they  describe  such  entitles  as  we  have  never  experienced, 
and  probably  never  could  experience?  Take  as  an  Instance,  any  one 
of  H.  O.  Wells'  romances,  such  The  Angel,  The  Sea-Lady,  The  First 
Men  In  the  Moon,  The  War  of  the  Worlds,  The  Invisible  Man,  The 
F\>od  of  the  Gods. 


CHAPTER  IV 

THE  INTELLECTUAL  ELEMENT  IN  JUDGMENT. 

The  Intellectual  Element.— What  we  understand  by  "validity 
of  judgment"  haa  not  been  exhausted  In  our  preceding  discus- 
sion.    We  have  seen  that  a  Judgment  Is  valid,  so  far  as  it 
really  forms  part  of  the  continuous  stream  of  sensory  experi- 
ence.   But  by  "validity"  we  ceitalnly  mean  more  thi.a  "form- 
ing part  of  a  continuous  sensory  stream,"    The  very  notlOD 
of  validity,  qorrectness,  accuracy,  truth,  or  however  we  name 
it,  seems  to  go  beyond  this  Idea  that  It  Is  "given"  to  us.    We 
contrast  a  Judgment  which  Is  valid,  not  with  one  which  Is  non- 
sensory  or   discontinuous,   but   with   a  Judgment   which   Is 
invalid,  unsound,  false.    For  the  great  majority  of  logicians, 
judgment  Is  concerned  not  so  much  with  the  sensory  side  of 
experience,  as  with  Intellectual  truth  and  falsity.     For  sen- 
sory continuity  they  would  substitute  Intellectual  consistency, 
and  would  throughout  appeal,  not  to  sensory,  but  to  Intel- 
lectual standards  of  validity.    From  continuity  as  such,  for 
example,  we  should  never  obtain  fixity,  deflnlteness.  clear-cut 
outlines.    Where  everything  Is  fluid,  as  In  a  process  charac- 
terised by  unbroken  continuity,— In  such  a  case  sameness, 
identity,  sharp  distinction,  i.  e.,  the  necessary  Instruments  for 
the  erection  of  complex  thought-structures,  are  absent.    Most 
logicians,  accordingly,  emphasise  the  Intellectual  side  of  Judg- 
ment, and  regard  sensation  as  furnishing  the  material  for 
thought,  while  Intellect   Introduces   Its  standards  Into  this 
otherwise  formless  material,  gives  It  definite  form  and  outr 
line,  Identity  and  distinctness,  and  on  the  basis  so  provided 
elevates  structures  In  which  Intellectual  Instruments  have  so 
far  transformed  the  original  material  that  a  great  tblnker  like 
Kant  can  assert  that  reason  only  apprehends  what  Itself  has 
constructed  In  accordance  with  Its  own  laws. 

It  Is  not  quite  correct  to  regard  sensation  as  merely  furnish- 
ing the  bare  material  for  thought.  The  sensory  consciousness 
is  no  pure  receptivity,  no  tabula  rasa  open  to  impressions  from 
any  and  every  kind  of  object  alike.    Aa  w6  have  Men.  it  la 


38        INTELLECTUAL  ELEMENT  IN  JUDGMENT 

already,  In  its  simplest  stages,  shot  through  with  instinct,  and 
presents  a  rudimentary  organisation.  The  animal  conscious- 
ness, for  instance,  is  not  a  chaos  of  unrelated  sensory  elements, 
but  is  an  organised  whole  In  which  even  abstract  general  ideas 
may  play  a  part.i  We  cannot,  therefore,  regard  all  organisa- 
tion of  the  sensory  elements  as  exclusively  the  work  of  intel- 
lect. And  yet,  what  the  central  nervous  system  secures  for 
the  animal  at  one  level  of  development,  the  intellect— perhaps 
here  also  by  means  of  the  nervous  system— secures  at  a  higher 
level.  The  function  of  intellect  is  undoubtedly  a  kind  of  organ- 
isation, but  an  organisation  which,  for  full  comprehension, 
must  be  regarded  from  the  view-point,  not  so  much  of  its  sur- 
vival value  for  the  organism,  as  of  its  conforming  to  its  own 
peculiar  standards,  which  are  intellectual  rather  than  bio- 
logical. 

In  order  to  obtain  a  clear  idea  of  the  nature  of  this  intel- 
lectual element  in  thought,  we  shall  trace  its  function  in 
Judgments,  starting  with  the  more  ^.naple,  and  proceeding 
gradually  to  the  more  elaborate. 

(A)  In  Judgment*  of  Perception.- In  "This  is  red,"  "The 
room  is  warm,"  and  similar  judgments,  the  Impulse  which 
induces  us  to  single  out  for  special  attention  the  redness  or 
warmth  of  some  object  which  stands  out  against  the  general 
sensory  background,  is  probably  not  Intellectual  interest.  It 
is  usually  some  feeling  which,  at  bottom,  is  instinctive.  Such 
feelings  lead  us  to  distinguish  between  background  and  stim- 
ulus, and  thus  to  organise  in  a  rudimentary  perceptual  rela- 
tion "This"  and  "red,"  or  "The  room"  and  "warm."  But  at 
this  level  of  consciousness  the  distinction  is  not  clear-cut. 
The  one  is  not  yet  a  "background"  and  the  other  not  yet  a 
"special  stimulus."  Neither  has  as  yet  a  precise  Identity  in 
virtue  of  which  they  are  distinguished  sharply  and  clearly 
from  one  another  and  deliberately  set  over  against  each  other 
in  an  intellectually  self-conscious  act  of  thought.  The  intro- 
duction of  such  standards  as  "Identity,"  "difference,"  "dis- 
tinction within  a  wider  whole  which  unifies,"  etc.,  in  a  word, 
the  raising  of  the  vaguely  felt  organisation  of  sensory  con- 
sciousness to  a  higher  power.  Is  the  work  of  intellect.  Fur- 
thermore, if  we  have  any  reason  to  mistrust  our  Judgment,  as 


J  Cf.  Wundt,  Loglk,  3d  edition.  Vol.  I,  chapter  1,  sects.  2-4.    Cf.  also 
Krdmann,  Log»,  2d  edition,  chapters  11-14,  pp.  66  and  71. 


IN  PERCEPTUAL  JUDGMENTS 


39 


when  the  object  is  only  dimly  Been,  or  when  our  conclusion  Is 
denied  by  a  second  person,  in  such  cases  the  critical  self-con- 
sciousness with  which  we  take  especial  notice  and  make  a 
deliberate  Judgment,  is  intellectual,  and  involves  reference  to 
intellectual  standards,  which  must  be  conformed  to  before  we 
are  satisfied.  In  such  cases  the  Judgment  is  accepted,  not 
merely  as  conforming  to  sensory  apprehension,  but  as  fitting 
into  a  system,  an  organised  whole,  of  Judgments  of  the  kind 
in  question.  In  perceptual  Judgments  this  reference  to  a 
wider  system  of  perceptual  thought  is  not  clearly  present, 
unless  our  conclusion  is  challenged.  But  it  is  always  a  part  of 
the  intellectual  background,  and  if  asked  to  Justify  our  Judg- 
ment, there  is  always  some  direct  reference  made  to  this  sys- 
tematic, sRlf-consistent  unity  of  our  thought. 

Let  us  emphasise  the  difference  still  further.  Sensory  appre- 
hension of  "This,"  "red,"  "warm,"  etc.,  is  vague,  not  precise, 
without  outlines,  not  clear-cut,  and  forms  part  of  a  living 
stream  of  consciousness  which  extends  continuously  from  the 
focal  present  in  many  directions  without  limit.  Intellectual 
apprehension  of  the  same  qualities  is  sharply  defined,  an 
apprehension  of  entities  taken  out  of  the  stream,  and  delimited 
against  each  other  in  such  a  way  that  their  natures,  that 
which  makes  them  what  they  are  known  to  be  and  distin- 
guishable from  what  they  are  known  not  to  be — stand  out  as 
clearly  envisaged  identicies.  Sensory  apprehension  is  an 
awareness  of  qualities  in  the  living  kaleidescope  of  flowing 
consciousness.  Intellectual  apprehension  is  the  result  of  an 
analysis  which  takes  the  constituent  elements  out  of  their 
movement  in  the  kaleidescope  and  subjects  them,  one  by  one, 
to  the  scrutiny  of  our  mental  microscope,  and  studies  them  in 
their  own  individual  natures,  as  well  as  in  their  sharply 
defined  relations  to  other  contrasted  elements.  For  sensory 
apprehension,  every  moment  of  our  changing  life  is»neio,  a 
variegated  texture  of  experience  in  which  no  element  is  ever 
apprehended  a  second  time  in  quite  the  same  setting.  Just 
as  we  cannot  step  into  the  same  stream  twice,  because  the 
water  into  which  we  stepped  before  is  now  washed  away 
down-stream,  so  the  red  which  we  experience  today  is  not 
the  same  as  the  red  which  we  experienced  yesterday.  Exter- 
nal conditions  have  changed;  we  also  have  changed.  Varium 
ct  mutabile  semper  homo.  For  intellectual  apprehension,  on 
the  contrary,  all  is  fixed  and  definite.    The  redness  of  a  sen- 


40         INTELLECTUAL  ELEMENT  IN  JUDGMENT 


Bory  experknce  is  abstracted  from  its  sensory  context,  is  cut 
off  and  fixed  by  the  mind;  and  for  the  intellectual  elaboration 
of  perceptual  experiences  we  use,  not  directly  apprehended 
sensory  elements,  but  a  kind  of  mental  counters,  not  a  par- 
ticular red  or  warm,  but  universalised  qualities,  red-ne<fl, 
warm-ne««,  qualities  that  never  were  on  sea  or  land,  artificial 
entities,  abstractions,  non-living,  discontinuous,  conceptual 
identities.  The  function  of  intellect  in  Judgments  of  percep- 
tion is  thus  to  introduce,  into  the  continuity  of  sensory  expe- 
rience, ideals  of  identity,  difference,  and  organisation.  The 
elements  thus  hewn  out  with  our  mental  hatchet  are  so  trans- 
formed that  they  constitute  portions  of  an  intellectual  system, 
amenable  to  standards  of  consistency,  systematic  unity,  and 
identity. 

(B)  in  Judgments  of  Experience. — In  "The  freight  trains 
crossing  the  bridge  grow  more  troublesome  every  year,"  and 
similar  Judgments,  the  sensory  element  consists,  as  we  have 
seen,  in  so  extending  the  focal  consciousness  of  the  low  rum- 
ble as  to  include  in  one  continuous  experience,  not  only  the 
spatially  distant  train  of  the  present,  but  also  the  temporally 
distant  trains  of  the  past.  The  associations  from  past  expe- 
rience, by  the  aid  of  which  this  is  accomplished,  are  fused 
with  the  focally  present  rumble-sensation,  and  constitute  an 
integral  portion  of  the  unbrokenly  continuous  sensory  con- 
sciousness, the  complex  perceptual  Judgment  which  we  call  a 
judgment  of  experience.  Certain  elements  in  the  Judgment 
appeared  to  us  to  be  definitely  intellectual,  especially  the  "com- 
parison" of  the  past  trains  with  the  present  rumble.  For  the 
rest,  the  interpretation  of  the  rumble  as  a  present  train,  and 
the  recall  of  past  trains,  together  with  associated  feelings  of 
annoyance  at  the  disturbance  so  occasioned — all  this  might 
well  take  place  on  the  sensory  level  of  consciousness.  In  the 
usual  run  of  things,  such  a  Judgment,  expressing,  as  it  does, 
mere  general  annoyance  at  being  disturbed,  would  not  tend  to 
rise  much  above  the  sensory  level.  But  where  it  is  thought 
advisable  to  establish  such  Judgments  of  experience  more 
firmly,  or  where  we  are  not  content  with  a  vague  general 
impression  but  insist  on  investigating  further  the  phenomenon 
in  question — in  such  cases  we  raise  the  Judgment  to  a  higher 
power  by  introducing  exact  intellectual  standards. 

How  is  this  accomplished?  We  analyse  or  split  up  the  con- 
tinuous experience  into  a  number  of  special  cases  of  trains-on- 


IN  EXPERIENTIAL  JUDGMENTS 


41 


the-bridge,  and  pass  these  special  cases  in  review,  one  by  one, 
noticing  in  each  case,  as  well  as  we  can,  the  comparative 
amount  of  disturbance  thus  caused.  The  distinction  of  these 
special  cases  from  one  another,  and  the  careful  attention  to 
the  disturbance  occasioned  by  each  one,  considered  by  itself, 
gives  us  a  far  clearer  basis  for  our  comparative  Judgment  as 
to  the  increase  of  the  disturbance  in  (luestion.  The  intellectual 
standards  thus  introduced  are  (1)  identity — ^the  introduction 
of  which  gives  us  units  suflSciently  equal  or  identical  for  com- 
parative purposes,  viz.,  the  individual  train-disturbances;  (2) 
difference — the  introduction  of  which  enables  us  to  separate 
out  and  distinguish,  both  from  one  another  and  from  expe- 
riences which  are  irrelevant,  the  various  unit-experiences  on 
which  the  judgment  is  based;  and  (3)  organisation — the  intro- 
duction of  which  enables  us  so  to  classify  and  arrange  these 
disturbance-units  within  the  wider  system  of  our  general  expe- 
rience, that  we  can  conclude  as  to  the  increasing  annoyance, 
within  that  system  taken  as  a  whole,  of  the  rumble  due  to 
the  passing  trains.  In  place  of  the  continuity  and  vague  flow 
of  actual  sensory  experience,  we  thus  have  sharply  differen- 
tiated, isolated  train-disturbance  experiences,  compared  with 
one  another  in  the  light  of  general  principles  of  organisation. 
The  clearness  thus  introduced  is  due  to  a  definite  transforma- 
tion of  the  original  experiences,  and  the  intellectual  side  of 
judgment  is  based  always  upon  elements  thus  torn  from  their 
living  context  and  fixed,  universalised,  organised  on  princi- 
ples, not  of  sensory  continuity,  but  of  strict  relevance,  con- 
sistency, conformity  to  intellectual  standards  of  systematic 
unity  and  truth.  It  is  in  this  way  that  bare  sensory  expe- 
rience is  taken  up  into  the  structure  of  an  empirical  science 
based  on  judgments  of  experience. 

(C)  In  Symbolic  Judgments. — In  "Rome  was  occupied  by 
Caesar"  and  similar  Judgments,  the  sensory  side  consists  of 
elements  taken  from  different  strata  of  our  conscious  life  and 
so  re-arranged  as  to  present,  with  something  of  the  warmth 
and  intimacy  of  personal  experience,  an  analogy  to  the  expe- 
riences actually  lived  through  by  Caesar  and  the  citizens  of 
Rome  at  the  time  of  which  we  are  reading.  The  nature  of 
the  part  played  by  intellect  is  here  conspicuously  plain.  In 
the  taking  elements  from  different  experiential  strata,  i.  e.,  in 
the  tearing  from  their  living  contexts  what  we  need  fdr  our 
purposes  of  construction,  we  clearly  see  the  introduction  of 


rii*i/^iiivj 


;    />' 


42         INTELLECTUAL  ELEMENT  LM  JUDGMENT 


the  standard  of  Identity.  With  the  Idea  of  one  Identical  expe- 
rience-type In  mind,  we  pass  in  review  the  scenes  from  our 
past  which  association  presents,  and  single  out  only  what 
passes  the  test  and  conforms  to  our  standard.  By  Introduc- 
ing the  standard  of  difference,  we  are  able  to  distinguish  and 
omit  from  the  reconstruction  everything  In  the  experiential 
context  which  is  irrelevant  to  the  demands  of  Identity. 
Finally  the  standard  of  organisation  enables  us  so  to  reor- 
ganise these  mutilated  experiential  fragments,  as  to  recon- 
struct something  consistent  with  the  wider  system  of  life 
which  extends  from  the  present  to  the  time  of  Caesar,  and  is 
guided  in  detail  by  the  text  of  our  history  book. 

In  symbolic  judgments  there  is,  however,  yet  further  evi- 
dence of  Intellectual  transformation  of  the  original  experi- 
ences.   The  unit  here  is  not  merely  the  Isolated  triumph  and 
panic-experiences,  but  Is  something  still  more  artlflcial,  still 
more  conventional.    So  far  as  our  judgment  is  an  expansion 
on  the  basis  of  the  printed  symbols  before  us,  the  ultimate 
units  are  these  symbols  themselves.    It  is  on  the  apprehension 
of  these  devitalised,  conventionalised,  universallsed  elements 
that  our  reconstruction  of  the  meaning  of  what  we  read  Is 
ultimately  based.    Perhaps  we  can  realise  the  part  played  by 
such  conventional  symbols  more  clearly  in  a  different  instance. 
Take  the  case  of  a  problem  about  ducks,  or  workmen,  or  time- 
pieces, solved  by  simultaneous  equations;  take  the  case  of  the 
distance  of  a  ship  at  sea,  discovered  by  an  appeal  to  trigono- 
metry; take  any  case  of  the  movement  of  bodies,  worked  out 
In  mathematical  physics.     In  all  such  cases,  the  raising  the 
problem  from  bare  sense-experience  to  the  intellectual  level 
means  the  substitution  of  Identical,  conventionalised  elements 
In  place  of  the  original  continuity  of  life,  and  it  is  on  the 
organisation   of  such  symbols,  strictly  treated  as  such,  that 
the  certainty  of  the  conclusion  depends.     In  taking  up  our 
sensory  experiences  into  the  structure  of  empirical  science, 
an  enormous  part  is  played  by  the  introduction  of  such  con- 
ventional identities,  and  it  Is  hardly  too  much  to  say  that  our 
experiences  admit  of  scientific  manipulation  only  so  far  as 
they  can  be  organised  and  formulated  in  terms  of  such  sym- 
bols. 

(D)  In  Transcendent  Judgments.  Transcendentjudsnients, 
as  we  have  see*,  eonstltute  a  kind  of-exteiuied._symbollcjudg- 
ment.    The  elements,  for  instance,  from  which  we  conctruct 


IN  TRANSCENDENT  JUDGMENTS 


43 


our  concept  of  the  "infinite  attributes  of  Ood,"  are  taken  from 
our  own  experience,  and  the  resulting  ideal  represents  man 
writ  large — so  large  as  to  extend  to  infinity,  i.  e.,  infinite 
knowledge,  infinite  power,  infinite  Justice,  etc.  In  symbolic 
Judgments  the  conventional  identities  separated  out  and  organ- 
ised  still  retain  Bome  relation  to  our  experience,  and  it  is  from 
their  fringe  of  associations  that  they  have  meaning  for  us. 
That  is  to  say,  the  conceptual  identities  on  which  the  Judg- 
ment  is  based  are  not  entirely  cut  loose  from  experience;  it  li 
mutilated  fragments  which  we  put  together,  torn,  if  we  will, 
from  the  living  experiential  context,  but  still  retaining  some 
semblance  of  life,  some  clinging  strands  which  bind  them  to 
our  personality  and  make  them  ours.  In  that  extension  of 
the  symbolic  Judgment  which  we  call  transcendent,  however, 
this  relation  is  reversed.  Our  experience  is  here  regarded  as 
an  isolated  fragment  torn  from  its  true  place  in  the  Infinite 
Experience;  to  consider  it  as  our  own,  as  constituting  a  finite 
unity  in  itself  is,  for  transcendent  thinking,  a  fundamental 
error.  We  must  learn,  on  the  contrary,  to  view  everything  . 
sub  specie  aeternitatis.  It  is  the  Divine  Experience,  of  which 
we  can  construct  the  outlines,  which  is  real  and  concrete;  it 
is  our  sensory  experience,  with  its  continuity  in  space  and 
time,  which  is  fragmentary,  riddled  with  contradictions, 
unreal,  abstract.  To  arrive  at  metaphysical  truth  we  must 
start,  indeed,  with  our  human  experience;  but  by  strictly 
introducing  the  standards  of  identity,  difference,  and  organ- 
isation— far  more  strictly  than  in  experiential  and  symbolic 
Judgments — we  pass,  step  by  step,  from  the  ideas  of  human 
goodness,  human  knowledge,  and  human  power,  to  greater- 
than-human,  and  finally  to  ideas  of  absolute,  infinite.  Divine  f 
goodness,  Divine  knowledge.  Divine  power.  It  is  by  the  strict  ^ 
introduction  of  these  intellectual  standards  that  we  not  merely  / 
reach  the  extreme  limit  of  possible  human  development  in  > 
goodness,  etc.,  but  ultimately  cut  ourselves  loose  from  the  -* 
remaining  strands  which  bind  us  to  humanity,  and  arrive  at\ 
ideas  which  far  transcend  these  in  dignity  and  power.  We 
use  these  intellectual  standards  as  a  kind  of  tower  by  which 
to  climb  the  steep  ascent  of  heaven.  After  the  top  of  the 
tower  is  reached,  in  physical  reality  we  could  mount  no  higher: 
but  knowledge  is  not  a  physical  tower,  and  has  no  such  limi- 
tations. From  the  purely  human  standpoint,  it  would  seem 
as  though  the  more  strictly  we  introduce  the  standards  of 


44         INTELLECTUAL  ELEMENT  IN  JUDGMENT 

Identity,  difference,  and  organisation,  the  more  attenuated 
becomes  the  living,  sensory  experience  with  which  we  start, 
and  the  more  formal,  artlflcial,  and  devitalised  become  the 
concepts  which  we  thus  construct,  until  flually  the  symbol  Is 
cut  loose  from  life  as  we  know  It,  and  sense  Is  lost  In  Intel- 
lectual vision.  For  the  metaphysician,  on  the  contrary,  this 
death  to  sense  is  the  beginning  of  Intellectual  life,  and  in  the 
ultimate  conatruetions  of  transcendent  thought  we  dhake  off 
the  fetters  which  bind  us  to  the  earth  below,  and  become  one 
with  the  Ideal  which  Is  also  the  only  real,  and  by  way  of 
the  intellectual  love  of  God,  enter  directly  Into  the  Divine 
Experience. 

Conclusion.  The  Function  of  int«llect.~If  we  now  put 
together  the  results  of  our  enquiry  In  the  present  chapter,  we 
realise  that,  as  in  other  spheres  of  life,  so  also  In  the  realm 
of  thinking,  the  f unct]jyj^jj£_[jntelJect  Is  to  organise  our  life- 
processes  and'  make  them  significant  and  rational.  The  con- 
text of  living  sensory  experience  contains  much  which  is  Irrel- 
evant and  accidental,  due  to  considerations  of  place  and  time. 
Our  Intellectual  analysis  leaves  us  with  sharply  differentiated 
Identities,  taken  out  of  this  context  and  stripped  of  al!  Irrel- 
evancles— timeless  and  placeless  entitles,  mental  counters 
which  can  be  put  together  in  accordance  with  the  demands  of 
systematic  unity.  Out  of  theste  elements  we  proceed  to  build 
up  au  edifice  of  thought,  a  structure  based  on  principles  which 
are  intellectual  rather  than  sensory.  Ii  is  like  Introducing 
the  card-index  system  Into  our  business— in  this  case,  the 
business  of  thinking.  We  can  now  take  hold  of  our  experi- 
ences, sort  them  out  and  handle  them,  shuffle  and  manipulate 
them  In  such  a  way  as  to  gain  all  the  advantages  of  scientific 
efficiency;  and  the  resulting  clarity  and  distinctness  are 
undoubtedly  a  real  gain. 

But  there  is  another  side  to  this  process  of  Intellectual 
analysis.  Something  has  been  lost  which  can  not  be  replaced. 
The  elements  Into  which  we  have  analysed  our  experience  are 
no  longer  fluid  and  living.  They  are  discontinuous,  fixed, 
rigid,  lifeless.  They  are  like  the  separate  pictures  which  a 
movlng-plcture  artist  puts  together  to  represent  some  drama 
of  real  life.  The  utmost  which  the  scientist  can  do  In  order 
to  visualise  Intellecluaily  the  life  which  he  has  split  up  Into 
fragments,  Is  to  put  together  the  separate  pieces  In  such  a 
way  as  to  simulate  the  original  movement  and  continuity.    But 


4r^<J^^A-^^^^ 


CONCLUSION 


4S 


the  result  li  always  Jerky,  tmnatural,  interrupted  by  flaihea, 
by  sudden  transitions,  by  small  flaws  in  the  film.  When  all 
Is  done,  it  rptnains  artificial,  mechanical,  a  photographic  imi- 
tation of  life.  The  scientist  Is  like  a  child  with  a  toy  which 
he  has  taken  apart.  He  understands  now  how  it  works,  but 
not  all  the  king's  horses  and  all  the  king's  men  can  put 
together  that  unsightly  heap  of  torn  flesh  and  dissected  organs 
which  was  once  a  livlns  frog  cr  embryo  chicken.  Thus  we^ 
see  that  the  introduction  of  intellectual  standards  of  identity,^' 
difference,  and  organisation  giveti  us  clearness,  certainty, 
science;  but  at  the  same  time  we  realise  that  this  clearnesi'^ 
has  been  bought  with  a  price:  and  it  is  a  question  how  far 
the  transformations  wrought  by  intellect  are  legitimate. 
Before,  however,  entering  upon  this  question— the  general 
question  of  validity— we  must  study  more  in  detail  what  is 
meant  by  Identity,  difference,  and  organisation. 


FOR  FURTHBR  RBADINO 

J.  Dowey.  eaaayt  in  EaptrUmental  Logtv.  pp.  220-220.  H.  Lotie, 
Logk;  pp.  10-18.  A.  RIehl,  Der  phUotophUche  KriUcUmui.  Vol.  II 
rhapter  I.     W.  VPundt.  Logik.  (3rd  Edit.),  pp.  74-00. 

EXERCISES 

1.  What  precisely  are  the  intellectual  elements  In  the  following: 
That  Huli  looks  oM.  These  nasturtiums  have  an  unpleasant  odor. 
Thp  corn  grows  larger  here  In  the  sun  thnn  what  I  see  there  In  the 
shade? 

2.  What  precisely  are  the  Intellectual  elements  In  the  followlnR 
JiidRments:  What  we  call  "robins"  are  usually  starllngn.  Mr.  X't 
hand-writing  Is  neariy  always  Illegible.  In  the  more  northerly  States, 
a  closed  sun-porch  Is  of  more  use  thnn  an  open  screened-ln  porch? 

3.  Wihat  precisely  are  the  intellectual  elements  In:  There  la  no 
Royal  Road  to  anccese.  Income:  $100.00;  expenditure:  $00.09: 
result:  happlntMs.  Expenditure:  $100.01:  result:  misery.  According 
to  results  based  upon  statistics,  T  should  expect  three  members  of  this 
class  to  receive  the  grade  At  . 

4.  What  precUc:y  are  the  Intellectual  elements  in  the  following: 
Whether  It  falls  within  the  sphere  of  potwible  experience  or  not.  the 
world  mutt  be  rational,  through  and  thrt^ngfa.  I  solved  the  riddle  of 
the  universe.    Virtue,  though  chained  to  earth,  will  s JU  live  free !  I 


CHAITER   V 


IDENTITY. 


Identity  or  Samonett.— What  do  we  m.an  by  "Identltv"? 
We  should  usually  say  that  any  one  thlnj?  «r  Idea  la  Identical 
with  Itself,  IS  the  self-same  thing  that  It  is:  beamy  Is  beauty, 
X  =  X,  '!tr.  Where  we  have  what  appear  to  be  two  entitles, 
we  shotufl  tall  them  Identical  If  they  were  the  game  In  all 
respects  »•  r/,.  two  triangles  on  the  same  base  and  with  the 
same  aw?x  .vouid  coincide  or  fall  together  absolutely.  They 
would  •.^>'  Identical,  and  mken  strictly  we  might  maintain  that 
there  was  only  one  triangle  pr^ent.  Identity  thus  excludes 
diversiiy  or  illfference;  so  far  as  entitles  are  different,  they 
may  be  equal,  bur  can  never  be  strictly  Identical.  E.  g., 
r-i  —  yi=  i.r+yj  x  —  y;.  Both  sides  of  this  equation  lead 
to  the  same  result:  but  the  Intellectual  operations  of  squaring 
and  subtracting,  on  the  one  side,  are  balanced  by  different  oper- 
ations on  the  other,  viz..  addition  within  brackets,  subtraction 
within  brackets,  and  multiplication  of  complexes.  The  two 
sides  of  the  equation  are  thus  equal,  but  not  absolutely  the 
same,  not  identical 

Let  us  apply  this  to  logic.  We  have  stated  that  Intellect 
introduces  identity  as  a  kind  of  standard  for  organising  our 
otherwise  somewhat  ihaotlc  sensory  experience.  This  means 
that  Intellect  singles  out  from  the  heterogeneous  mass  of 
sensory  elements  those  whi(  h  are  of  one  and  the  same  kind, 
and  regards  these  as  units,  as  identical  points  with  reference 
to  which  our  thought  buitds  up  Its  characteristic  chains  of 
judgments  and  Inferences.  The  elaborate  structures  of  science 
and  art.  Let  us  consider  'n  detail  how  this  iniroductlon  of 
Identical  points  of  referem      takes  place. 

(A)  In  Judgments  of  Perception.— Take  su<"h  a  case  as 
"This  room  is  warm."  W.  are  seated  in  the  room,  and  direct 
our  thought  to  the  temperature,  ne.^lecting  the  gsomstrlcal. 
social,  and  other  features  or  the  room.  Omitting  from  con- 
sideration all  other  elemf  ts  in  the  sensory  environment,  we 
single  out  only  such  stlm  ill  as  hai^e  one  and  the  same  refer- 

46 


IN  PERCrPTUAL  JUDGMENTS  # 

ence,  <.  e.,  atimull  which  posseas  temperature  value.    In  thU 
way  we  come  to  Judge  that  the  room  is  warm.    The  warmth 
of  the  room  is  thu«  one  unit  within  the  Judgment,  an  identical 
point   of    reference    around    which    our    thought,    which    was 
previously  va«ue  and  Huld,  (ryatallBes  and  becomes  clear  and 
precise.    Another  such  unit  within  the  Judgment  Is  undoubt- 
;<ll.v    the  room."    This  unit  Is  constituted  by  direction  of  our 
thought  to  those  features  of  our  sensory  environment  which 
all  alike  are  connected  with  the  place  where  we  are  seated. 
rather  than  to  the  hundred  and  one  other  elements  which 
might  similarly  have  been  selected  as  starting-points  for  Judg- 
ment: c.  g.,  our  work,  our  furnltiire,  other  people  in  the  room. 
In  this  way.  In  place  of  the  vague  fluctuating  mass  of  rela- 
tively unorganised  sensations,  we  come  to  have  a  new  organ- 
ised unity,  our  Judgment,  are    within  this  Judgment  two  spe- 
'  lal   unities,   the   starting-point    and    the    end-point    of    our 
thought.     These  two  special  units,  "The  room,"  with  which 
we  start,  and  the  "Is  warm."  which  represents  our  further 
determination   of   "The   room,"— are   rei-ognlsed   by   logicians 
under  the  names    logical  subject"  or  «,  and  "logical  predicate" 
or  P.  8  means  the  subject  of  discourse,  what  we  are  thinking 
about,  and  P  means  what  we  Judge  or  think  about  B.    They 
are    thought   with    reference    to    one    another;    the    room    Is 
thought  of  as  being  warm,  and  warmth  is  thought  of,  not  in 
a  general  way,  by  Itself,  but  In  definite  relation  to  the  room. 
The  logical  distinction  between  i8  and  P  should  not  be  con- 
fused with  the  grammatical  distinction  between  subject  and 
in.'dlcate  of  a  sentence.    One  and  the  same  thought  can  have 
a  hundred  modes  of  grammatical  or  rhetorical  expression,  and 
It  Is  easily  possible  for  S  to  be  expresseu  by  the  predicate 
of  a  grammatical  sentence,  and  for  P  to  be  expressed  by  the 
grammatical  subject.    Usually,  Indeed,  there  is  a  tendency  for 
.V  and  the  grammatical  subject  to  coincide;   but  there  is  no 
necessary  connection  between  the  order  of  thought  and  the 
order  of  verbal  expression.    Consider,  for  example,  "It  is  warm 
In  the  room,"  "Warmth  Is  the  most  pronounced  feature  of  the 
room,"  "Warm  1st  das  Zimmer. '     These  are  three  different 
ways  of  expressing  one  and  iho  barae  thought,  and  If  "The 
room"  IH  the  subject  of  dlseeur«ir,  it  remains  the  subject  of 
discourse  whatever  the  grammatical  or  linguistic  vehicle  of 
expression.  Or  again,  If  I  am  discussing  the  subject  of  warmth 
so  that  "warm"  or  "warmth"  Is  S,  the  subject  of  discourse' 


48 


IDENTITY 


,ht  say,  "Warm  Is  .  .  .  why,  the  room  is  warm, 
wttf  fire  Is  warm,  the  water  from  this  faucet  is  warm,  etc." 
In  this  case,  "warm"  still  represents  the  logical  subject,  while 
"the  room,"  "the  fire,"  "the  water  from  the  faucet,"  etc.,  rep- 
resent new  logical  predicates,  units  singled  out  of  the  sensory 
environment  in  order  to  explain  or  determine  further  what 
we  are  thinking  about,  viz.,  "warm."  Thus  we  see  that  8 
and  P  are  independent  of  grammatical  distinctions,!  and  lit 
the  case  of  perceptual  judgments,  we  can  conclude  generally 
that  our  thought  organises  the  vague  flow  of  sensory  con- 
sciousness by  crystalising  around  two  points  of  reference,  a 
starting-point  and  an  end-point  of  judgment,  8  and  P,  respec- 
tively. This  introduction  of  the  standard  of  identity  gives  us 
clearness,  deflniteness,  and  precision,  an  intellectualised  basis 
for  the  further  organisation  of  our  thought. 

(B)  in  Judgments  of  Experience. — In  such  a  judgment 
as  "The  freight-trains  crossing  the  bridge  grow  more  trouble- 
some every  year,"  we  are  seated  at  work,  and  are  disturbed 
by  the  rumble  of  a  passing  train.  Our  reaction  to  this  disturb- 
ance expresses  itself  in  a  feeling  of  annoyance,  and  with 
this  feeling  in  mind,  we  omit  from  consideration  all  other 
elements  in  the  environment,  and  single  out  from  -  experi- 
ences only  such  as  have  one  and  the  same  reference,  tig.,  com- 
parative annoyance-value  of  this  type.  In  this  way  we  come  to 
judge  that  the  disturbances  are  growing  more  annoying  every 
year.  The  increasing  annoyance  of  such  disturbances  thus 
constitutes  one  unit  within  the  judgment— an  identical  point 
of  reference  around  which  our  experiences,  which  were  pre- 
viously fluid,  vag'ie,  and  somewhat  chaotic,  become  organ- 
ised, determinate,  flxed.  In  place  of  the  vague  continuity 
of  annoyed  feeling,  we  have  reached  a  definite  conclusion, 
in  which  we  can  rest.  Another  such  point  of  reference  is 
undoubtedly  the  disturbance-due-to-freight-trains.  This  fur- 
nishes the  starting-point  of  our  judgment,  and  it  is  of  this 
freight-train  disturbance  that  we  judge,  that  it  "is  growing 
more  troublesome."    As  a  unit  of  reference  it  is  constituted 


»  We  may  further  suspett  that  In  reading  or  bearing  a  grammatical 
sentence  taken  out  of  Its  context.  It  Is  ImpoBsIble  to  say  with  certalbty 
What  is  the  subject  of  discourse.  Prom  such  a  statement  as  "That 
'»  a  *VS^'"  ♦*ken  by  Itself,  It  Is  Imr^sslble,  apart  from  the  context, 
to  decide  whether  ft  Is  "trees"  which  are  being  Hpoken  of.  In  wUch 
case  'lYee"  Is  S,  and  "That"  is  P,  or  whether  "that  oWsct"  Is  being 
discussed,  In  which  case  "That"  is  S,  and  "Is  a  tree"  Is  P. 


IN  EXPERIENTIAL  JUDGMENTS  49 

by  concentration  of  our  thought  In  the  one  direction,  and  by 
omitting  from  consideration  our  work,  the  room  we  are  in, 
and  the  hundred  and  one  other  featureff'of  the  sensory  envi- 
ronment In  which  we  might  hare  been  especially  interested. 
In  this  way.  In  place  of  the  general  attitude  of  attention 
to  our  work,  with  vaguely  felt  impressions  coming  in  through 
all  the  avenues  of  sense  in  an  unorganised  manner,  we  come 
to  have  a  new  organised  unity,  our  Judgment  concerning  the 
increasing  annoyance  of  train-disturbances.  Within  this 
judgment  we  have  two  subordinate  unities,  (1)  the  starting- 
point  of  our  thought,  viz.,  the  disturbance,  and  (2)  the  end- 
point,  viz.,  that  It  Is  growing  more  troublesome.  The  dis- 
turbance, due  to  freight-trains  is  thus  the  subject  of  discourie, 
or  8,  andvthe  thought  that  such  disturbances  "are  growing 
more  troublesome  every  year"  Is  what  we  Judge  of  iSf,  i.  e.,  is 
the  logical  predicate,  P.  The  introduction  of  the  standard  of 
Identity  thus  gives  us.  in  place  of  the  irrelevant  and  chaotic 
elements  which  form  part  of  our  continuous  experience  merely 
because  they  have  happened  to  us,  for  the  most  part  as  mere 
events  without  rhyme  or  reason— in  place  of  this  relatively 
unmeaning  and  unorganised  copMnulty,  the  Introduction  of 
identity  gives  us  c'earness,  relevance,  deflniteness,  an  intellect- 
uallsed  basis  for  the  further  organisation  of  our  thought. 

(C)  In  Symbolic  Judgments.— In  such  a  Judgment  as 
"Rome  was  occupied  by  Caesar."  we  are  reading  a  history 
book,  and,  in  order  to  realise  and  make  vivid  to  ourselves 
the  meaning  of  what  we  read,  we  summon  from  our  personal 
experiences  all  which  have  one  and  the  same  reference,  all 
which  in  some  way  bring  to  our  mind  feelings  of  panic  and 
triumph  suitable  to  the  occasion,  the  alarm  of  the  Pompeians 
being  balanced  by  the  triumph  of  Caesar's  friends.  In  this 
way  we  come  to  realise,  as  well  as  we  can,  what  "occupation" 
means,  and  thus  to  think  fully,  or  to  Judge,  with  full  under- 
etandlng  of  the  meaning  of  our  Judgment,  that  Rome  "was 
occupied  by  Caesar."  Was-occupied-by-Caesar  thus  furnishes 
one  unit,  one  point  of  reference  within  the  Judgment,  aroand 
which  the  rough  mass  of  associated  experiences  becomes  gradu- 
ally organised,  and  crystalises  in  definite  dear-cut  form.  An- 
other such  nucleus  of  organisation  lit  furnished  by  "Rome," 
the  general  scene  and  background  against  which  the  yarions 
episodes  of  Roman  history  successively  stand  cot  It  Is  the 
starting-point  of  our  Judgment,  and  is  consUtnted  by  th«  or- 


50 


IDENTITY 


ganisation  of  all  of  our  experiences  which  relate  in  any  way  to 
the  Eternal  City.  It  arises  in  our  minds  as  a  unit  of  reference 
when  we  direct  our  thought  only  to  such  elements  of  our  experi- 
ence as  are  connected  with  the  great  city  about  which  we  are 
reading,  to  the  exclusion  of  other  subjects  of  possible  interest. 
"Rome"  is  thus  the  subject  of  discourse,  the  S  of  our  judg- 
ment; "was  occupied  by  Caesar"  is  what  we  Judge  about 
Rome,  i.  e.,  is  the  logical  predicate,  P.2 

In  making  this  Judgment,  what  have  we  effected?  In  place 
of  the  general  attitude  of  mind  consequent  upon  reading,  with 
vaguely  continuous  sensory  impressions  coming  in  through 
eye,  ear,  etc..  and  vaguely  aroused  associations  from  past 
experiences,  unorganised  and  irrelevant  but  all  forming  part 
of  the  cross-section  of  our  conscious  life,  we  have  now  a 
sharply  distinguished,  clear-cut  unity,  the  judgment  that 
"Rome  was  occupied  by  Caesar."  Within  this  unity  we  have 
two  definite  unities,  ( 1 )  Rome,  the  background  of  our  history 
and  starting-point  of  our  judgment,  and  (2)  "was  occupied 
by  Caesar,"  the  new  determination  of  our  thought  of  "Rome," 
the  end-point  or  logical  predicate  of  our  judgment.  These  two 
units,  Rome  and  was-occupied-by-Caesar,  are  clear  fixation- 
points  introduced  as  identical  points  c!  reference  by  the  intel- 
lect, and  furnish  an  Intellectuallsed  basis  for  the  further 
organisation  of  our  thoughts,  as  we  build  up  for  ourselves 
an  adequate  conception  of  History. 

(D)  In  Transcendent  Judgments. — If  we  compare  the  logical 
subjects  in  the  various  types  of  judgment  considered  hith- 
erto, "The  room,"  "Freight-train-disturbances,"  "Rome,"  we 
notice  at  once  that,  while  all  alike  are  units  or  identical 
points  of  reference  within  their  respective  judgments,  yet 
the  later  ones  are  increasingly  complex.  "The  room"  is  a 
matter  chiefly  of  present  sensory  experience;  "Freight-trains" 
include  not  only  present  sensory  experience,  hut  also  the 
relevant  experiences  which  go  back  for  some  years;  and 
"Rome"  furnishes  a  centralising  nucleus  for  very  many  and 
very  complex  experiences.  So  too  when  we  compare  the 
logical  predicates.  "Warm"  is  a  relatively  simple  experience 
as  compared  with  "grow  more  troublesome  every  year,"  and 

a  It  l8  aiwnmed  In  the  text  that  It  is  a  "History  of  Rome"  which 
we  are  readlni;.  If,  however,  the  sentence  occurred  in  a  "Life  of 
Cjieaar,"  so  that  Caeaar  and  his  actions  constituted  the  main  itHbWt 
of  dtacourae,  then  "Caesar"  would  be  S,  and  "Rome-occupled-by-him" 
would  be  the  further  determination  of  this  subject,  which  we  call  P 


V-    c^. 


V^X' 


-f  yi'yuJ 


IN  TRANSCENDENT  JUDGMENTS 


51 


this  again  is  less  complex  than  the  innumerable  series  of 
experiences  which  are  organised  with  reference  to  the  idea 
of  "was  occupied  by  Caesar."  As  we  have  seen  before,  Judg- 
ments of  perception  are  organisations  chiefly  of  immediate 
sensory  experiences;  judgments  of  experience  include  also 
associations  from  past  actual  experience  of  the  subject  of 
discourse;  while  symbolic  Judgments  go  beyond  this,  and 
include  all  possible  experience,  t.  e.,  all  combinations  of  actual 
experiences  which  the  mind  can  construct  suitably  to  the 
occasion.  This  is  more  complex  than  what  we  And  in  the 
experiential  Judgment,  for  there  we  are  confined  to  those 
experiences  which  have  actually  occurred  in  the  combination 
in  question,  whereas  in  the  symbolic  Judgment  we  rearrange 
and  re-comblr  elements  originally  experienced  In  other  com- 
binations, anu  hus  have  a  much  larger  stock  of  experiences 
on  which  to  draw.  If.  then,  the  same  rule  is  exemplified  In 
transcendent  Judgments  also,  we  shall  expect  to  find  that  the 
identical  points  of  reference  introduced  into  this  class  of  Judg- 
ments are  the  most  complex  and  far-reaching  of  all. 

Consider  such  a  case  as  "God  is  a  substance  consisting  in 
infinite  attributes."    The  logical  subject  here  Is.  pres' -nably. 
"God."  and  the  logical  predicate  "is  a  substance  consisting  In 
infinite  attributes."    The  term  "God"  Includes  all  our  experi- 
ence, both  actual  and  possible,  and  is  thus  the  most  complex, 
all-inclusive  Idea  that  we  can  form.    And  if  we  go  still  further.' 
and  include  in  the  Idea  not  only  all  possible  human  experi- 
ence, but  also  the  thought  of  experiences  infinitely  wider  and 
deeper  than  anything  which  any  human  being  can  know,  we 
include  not  only  all  possible  human  knowledge,  but  go  beyond 
this,  and  launch  out  upon  the  infinite  ocean  of  the  barely 
thinkable  and  imaginable.     So  too  with  the  logical  predicate 
of  this  subject.     Not  only  spatial  and  mental  qualities  are 
ascribed  to  this  substance,  but  they  are  attributed  to  it  In 
an   infinite  degree,   including  all  we   could  ever  know,  and 
more.    And  further,  an  infinity  of  other  attributes,  each  one 
of  which  lies  In  the  great  Beyond,  beyond  anything  of  which 
we  finite  human  creatures  can  even  frame  a  concept,  are  also 
assigned  to  this  substance.     Thus  we  see  that  In  the  trans- 
cendent Judgment,  both  s  and  P  reach  the  limit  of  incluslve- 
ness.  the  extreme  limit  of  complexity. 

It  remains  to  ask  whether  it  is  by  using  the  principle  of 
identity  that  we  form  these  transcendent  concepts.     So  far 


52 


IDENTITY 


as  a  symbolic  Judgment  is  concerned,  so  far,  that  is,  as  out 
of  the  slireds  and  patches  of  our  experience  we  construct  an 
ideal  man,  a  man  writ  large,  if  we  will,  but  still  humanly 
possible,  still  man — so  far,  we  have  already  seen,  it  is  by 
selecting  from  our  experience  only  such  elements  as  have  one 
and  the  same  reference,  i.  e.,  by  introducing  the  standard  of 
identity,  that  we  construct  the  symbolic  concept  in  question. 
But  when  we  go  further,  when  we  transcend  the  humanly 
possible  and  construct  the  'ea  of  something  beyond  what 
we  could  experience,  some  lUg  infinitoly,  Divinely  perfect, 
not  man-writ-large,  but  GOD— do  we  reach  this  transcendent 
ideal  also  by  holding  fast  to  some  identical  point  of  reference, 
or  do  we  adopt  some  other  method? 

The  answer  is  that  here  also,  be}ond  experience  as  within 
It,  both  8  and  P  are  formed  by  the  aid  of  this  identity- 
standard.  The  point  of  reference  remains  one  and  the  same 
throughout.  It  is  the  idea  of  the  "absolutely  perfect."  So 
long  as  we  confine  ourselves  to  human  experience,  we  can 
only  attain  to  rough  approximations  to  this  standard,  and 
the  resulting  concept  falls  short  of  c;ir  ideal,  remaining  all 
too  human,  and  limited  by  human  imperfections.  When  we 
cut  ourselves  loose  from  the  limitations  of  experience,  we  do 
not  In  any  way  change  the  main  direction  of  our  thought: 
we  still  proceed  to  build  up  the  idea!  of  the  absolutely  per- 
fect. All  that  is  new  is  that  we  select  strictly  and  exclusively 
what  conforms  to  this  standard.  We  leave  out  of  the  picture 
those  aspects  of  human  nature  which  are  finite  and  imperfect, 
and  retain  only  the  formal  abstract  essence  of  goodness,  truth, 
power,  etc.,  and  even  add  the  purely  formal  idea  of  other 
attributes  not  exemplified  in  our  human  experience  at  all. 
Thus  we  see  that  in  the  realm  of  complex  feelings  which 
spread  out  over  the  whole  of  our  experience,  the  introduction 
of  the  standard  of  identity  enables  us  to  organise  our  experi- 
ences in  a  way  which  gives  us  at  least  clearness  and  pre- 
cision, and  furnishes  a  definite  basis  for  the  further  organi- 
sation of  our  thought. 

Conclusion:  The  Standard  of  Identity. — In  all  types  of 
Judgment,  then,  one  function  of  intellect  consists  in  selecting 
from  our  experiences  all  such  as  have  one  and  the  same 
identical  reference,  all  wht'^h  are  strictly  relevant  to  some 
definite  subject  of  discourse,  whether  the  field  is  sensory, 
experiential,  or  some  symbolic  or  transcendent  extension  of 


CONCLUSION 


53 


the  field  of  direct  experience.  By  introducing  this  standard 
of  identity-of-reference  we  come  to  have.  In  place  of  the  vague 
general  flow  of  sensory  consciousness  (1)  a  sharply  demarcated 
unity,  which  constitutes  the  Judgment  as  a  whole,  e.  g.,  "It  is 
warm  here,"  "This  -llsturbance  is  excessive,"  and  (2)  within 
this  new  field  two  subordinate  unities,  (a)  a  clearly  envis- 
aged subject  of  discourse,  or  logical  subject,  and  (b)  a  definite 
determination  of  that  subject,  viz.,  the  logical  predicate,  "is 
warm,"  "is  excessive."  In  this  way,  then,  in  place  of  an 
experience  determined  by  the  order  in  which  things  have 
happened  to  us — ^a  chance  medley  of  sensations,  wishes,  and 
feelings — we  Introduce  an  order  determined  by  unity  of  mean- 
ing, relevance,  and  identical  reference. 

FOR  FURTHER  READINQ 

B.  BoBanquet,  Logic,  Vol.  II.  pp.  206-208.  F.  H.  Bradley,  Principle$ 
of  hogic.pp.  131-135.  B.  Krdmann,  Logik.  (2nd  Edit.),  pp.  237-253. 
Chr.  Slgwart,  Logic.  Vol.  II,  pp.  24-30,  80-02.  W.  Wundt,  Logik.  (3rd 
Edit.),   Vol.   I,  pp.  552-553. 


EXERCISES 

1.  How  far  does  the  standard  of  Identity  enter  Into  the  following: 
This  mirror  Is  dn»t]r.    i  like  tbls  picture.    That  hurts? 

2.  How  far  does  the  standard  of  Identity  enter  lato  the  foUowin( : 
Children  are  a  Joy,  so  far  as  my  experience  goes.  The  card-Index 
system  has  Increased  the  efficiency  of  my  business.  The  cost  of  living 
has  steadily  gone  up  for  the  last  three  years? 

3.  How  far  does  the  standard  of  Identity  enter  Into  the  following : 
Sea-sickness  depends  upon  the  functioning  of  the  seml-clrcular  canals. 
Blerlot  was  the  first  man  to  cross  the  English  Channel  In  an  air-plane, 
t.lttle  Bo-Peep  has  lost  her  sheep? 

4.  How  far  does  the  standard  of  Identity  enter  loto  the  following : 
Things  In  themselves  are  the  underlying  ground  of  sense-perception. 
Oh,  for  a  mansion  In  the  skies!  A  form  of  unutterable  beauty 
appeared  to  me? 


CHAPTER  VI 

DIFFERENCE. 

Introduction   of   Difference.— What  do   we   mean  by  differ- 
ence?    "A  is  different  from  B"  means  that  A  Is  distinguish- 
able from,  other  than,  B:  A  and  B  are  diverse;  A  and  B  can 
be  separated!  from  one  another,  can  be  set  over  against  and 
opposed  to  one  another,  can  be  contrasted  with  and  denied 
of  one  another.    A  is  not  B.    A  and  B  are  not  the  same,  do 
not  constitute  an  absolute  unity,  an  Identity;  on  the  contrary, 
they   constitute   a   duality,   a    plurality.     They   are   not   one, 
but  at  least  two,  and  can  be  sharply  delimited  against  one 
another.     Stated  negatively,  each   Is  not   what  the  other  is; 
Btated  positively,  each  is  what  the  other  is  not.    Stated  nega- 
tively, an  electric  bulb  Is  different  from  a  typewriter,  because 
each  fails  to  possess  qualities  essential  to  the  functioning  of 
the  other.     The  bulb   has  no  keys,  no  ribbon,  no  place  for 
inserting  paper,  and  thus  cannot  be  used  for  the  same  pur- 
pose as  a  typewriter.    The  typewriter,  on  the  other  hand,  has 
no    transparent    surface,    no    wires,    no    connection    with    an 
electric   battery,   and   thus   cannot    be   used   to   illuminate  a 
room.     They   are   thus   sharply   distinguishable   or    different 
from  one  another      Stated  positively,  In  order  to  emphasise 
the   positive   element   on    which   the   differentiation   depends, 
each  has  Its  own  Identity,  Its  own  nature,  that  which  makes 
it  what  it  is.    The  bulb  has  the  transparent  surface  and  plat- 
inum wire,  the  machine  has  the  keys  and  ribbon.     Each  has 
the   qualities   which   fit   it   for   the   performance  of   its  own 
special  function,  and  It  Is  In  virtue  of  specialisation  or  differ- 
entiation  of  function  that  each   cannot   perform  the  other's 
function,  and  Is  thus  different  from  it.     If  we  apply  this  to 
logic,  we  see  that  "introduction  of  the  standard  of  difference" 
will    mean    splitting    up    the    stream    of    consciousness    Into 


»  Sennrated.  i.  r..  In  thi>u»rht.  not  nweasarlly  In  reality.  The  con- 
cave and  convex  aspects  of  one  and  the  same  curve  for  Instance,  can- 
not be  separated  liTactuaUty.  but  can  be  separated  In  thought,  and 
regarded  as  "different." 

54 


<7' '^li  ^Pv^-:  ^  C^  //-VT^  (i,,y 
IN  PERCEPTUAL  JUDGMENTS  af/o^^^if   ^tr^.**7 


^ 


identities  which  are  sharply  distinguished  from  and  con- 
trasted with  one  another.  Let  us  consider  more  in  detail 
what  this  means. 

(A)  In  Judgments  of  Perception.— Let  us  consider  such  a 
judgment  as  "This  room  is  warm."  Before  we  introduce 
intellectual  elements  into  our  thought  and  frame  a  judgment, 
our  consciousness  flows  evenly  at  the  sensory  level.  We  are 
seated  quietly  at  work,  and  a  cross-section  of  our  consciousr 
ness  reveals,  beside  the  complex  work-interest,  only  a  vague 
general  background  of  feelings,  incipient  impulses,  and  half- 
apprehended  sensatiens,  all  equally  without  distinction  con- 
tributing to  sweJl  tbe  fluid  undifferentiated  mass,  in  which 
no  difference,' no  clear-cut  outlines,  have  as  yet  been  intro- 
duced. 

What  change  occurs  when  we  introduce  difference?  In 
place  of  a  continuous,  undifferentiated  mass  of  sensations, 
feelings,  and  impulses,  we  have  the  distinct  sensation  of 
'warmth"  standing  out  in  sharp  contrast  over  against  our,^ 
previous  state.  This  sensation  forces  itself  upon  our  attention^ 
by  excluding  other  conscious  elements,  and  the  more  clearly 
we  become  aware  of  it,  the  more  sharply  do  we  distinguish 
it  from  the  general  sensory  background.  It  constitutes  a„^ 
nucleus  for  introducing  still  further  distinctions.  We  split  -' 
up  the '  stream  of  consciousness  into  elements,  among  which 
"the  room"  is  also  prominent.  "The  room"  is  "warm."  Per- 
haps it  ought  not  to  be  warm.  The  furnace  needs  attention, 
or  there  is  a  fire.  In  our  judgment  we  thus  have  two  elem- 
ents, "the  room"  and  "warm,"  analysed  out  from  the  general 
conscious  flow,  separated,  cut  off  and  fixed  by  the  mind  in  sharp 
distinction  from  one  another.  These  two  elements  are  what 
we  have  come  to  know  as  S  and  P.  In  the  previous  chapter 
we  considered  them  as  "identities"  constituted  by  the  posi- 
tive concentration  of  thought  in  some  one  direction.  In  the 
present  chapter,  we  are  considering  them  from  a  more  nega- 
tive aspect,  as  differentiated  or  distinguished  from  one 
another:  S  is  not  P,  and  P  is  different  from  S. 

Let  us  consider  what  this  means.  Suppose,  if  possible, 
that  8  and  P  were  not  distinct  from  one  another.  Take,  e.  g., 
such  a  statement  as  "The  room  is  the  room,"  "warm  is  warm." 
Such  "identical  propositions" — as  they  are  called — are  almost 
without  meaning.  As  we  approximate  more  and  more  to 
complete  absence  of  difference,  so  do  we  approximate  to  com- 


>  -^-^Vl 


IVV.^^ 


56 


DIFFERENCE 


plete  absence  of  thought,  of  Judgment.  If  the  end-point  is 
in  no  respect  different  from  the  starting-point,  then  we  have 
never  really  started:  there  has  been  no  movement  of  thought, 
no  mental  operation.  It  is,  in  fact,  only  where  8  and  P  are 
sharply  differentiated,  that  a  genuine  Judgment,  in  which 
something  is  actually  thought,  some  problem  solved,  some 
conclusion  reached — takes  place.  When  Pilate  says  "What  I 
have  written,  I  have  written,"  he  means  "What  I  have  written 
stands,  is  unalterable,  must  and  shall  remain  what  I  have 
made  it":  and  it  is  precisely  this  difference  between  8  and  P 
which  gives  us  the  movement,  the  living  element  essential 
to  meaningful  thought.  Thus  we  see  that  introduction  of  the 
standard  of  difference  into  our  thinking  is  vital  to  Judgment, 
and  results  in  giving  us  the  logical  £1  and  P,  no  longer  as 
mere  identities,  but  as  sharply  differentiated  identities,  clear- 
cut  elements  whose  distinctness  is  essential  to  the  intellectual 
organisation  of  our  experience. 

These  differences  hold  within  the  Judgment  itself.  But  we 
should  also  note  that  the  Judgment  as  a  whole  has  been  carved 
t  out  of  our  sensory  experience.  The  mental  hatchet  of  differ- 
"  ence  has  thus  separated  off  not  merely  the  8  and  P  of  logical 
thought,  but  also  the  Judgment  as  a  whole,  as  an  intellectu- 
alised  complex,  sharply  distinguished  from  the  previous  state 
of  mind. 

(B)  In  Judgments  of  Experience. — Consider  such  a  case  as 
"The  freight-trains  crossing  the  bridge  are  growing  more 
troublesome  every  year."  We  are  seated  at  work,  when  the 
distant  rumble  forces  itself  upon  our  attention.  At  once,  in 
the  place  of  the  steady,  even  flow  of  consciousness  in  the 
direction  of  our  work-interest,  we  have  opposition,  contrast, 
interruption.  The  in-breaking  sensation  interferes  with  and 
thwarts,  for  the  mi  mem,  our  work-interest,  and  is,  so  far, 
annoying.  If  our  consciousness  remains  at  the  sensory  level, 
we  experience  ualy  a  vague  general  sound-annoyance,  which 
comes  and  goes.  But  if  the  stimulus  persists,  or  is  very  loud, 
the  experience  tends  to  rise  to  the  level  of  an  intellectual  ised 
thought,  a  Judgment  in  which  difference  is  clearly  present. 
As  we  attend  more  and  more  to  the  rumble,  the  two  elements, 
(1)  of  what  the  annoying  rumble  means,  viz.,  freight-train- 
disturbances,  and  (2)  the  increasing  troublesomeness  of  such 
disturbances,  become  clearly  separated  out  and  differentiated 
in    our   minds.      The    train-disturbances    are    becoming   too 


IN  EXPERIENTIAL  JUDGMENTS 


57 


troubleaome;  they  ought  not  to  be  allowed  to  grow  worie; 
some  protest  muit  be  made.  The  steady,  even  flow  of  con- 
sciousness has  disappeared,  and  In  lU  place  we  have  sharply 
opposed  and  clearly  outlined  elements,  (1)  train-disturbances 
in  the  past  and  present,  and  (2)  the  thought  that  these  are 
growing  increasingly  troublesome. 

We  thus  have  a  Judgment  in  which  the  two  elemenU  which 
we  have  come  to  know  as  8  and  P  stond  out  prominently.    In 
the  preceding  chapter,  these  were  considered  positively,  as 
identities  Introduced  by  the  concentration  of  our  thought  in 
definite  directions.  At  present,  they  are  being  considered  more 
negatively,  as  different  from,  distinguished  from,  and  opposed 
to,  or  contrasted  with,  one  another.  They  are  contrasted  identi- 
ties. Bach  has  its  own  nature,  but  these  natures  are  different, 
and  it  is  the  meaning  of  this  difference  for  Judgment,  which 
we  are  trying  to  realise.  Suppose  there  were  no  such  difference. 
Suppose  8  and  P  coincided,  as  In  "The  freight-trains  crossing 
the  bridge  are  the  freight-trains  crossing  the  bridge."    Is  there 
any  valuable  element  of  meaning  about  such  a  statement? 
Would  any  one  seriously  regard  such  a  form  of  words  as 
expressing  a  Judgment,  an  act  of  thought  which  might,  e.  g., 
cause  the  thinker  to  be  treated  as  Intelligent  rather  than 
imbecile?    If  there  were  really  no  shade  of  differences  Intro- 
duced between  8  and  P,  If  they  strictly  coincided,  clearly  there 
would  be  no  act,  no  movement  of  thought,  no  discovery,  no 
new  step,  no  solution  of  a  problem,  no  Intelligent  behavior  at 
all.    In  other  words.  In  order  to  form  a  Judgment,  to  think 
something  which  Is  meaningful,  significant,  to  advance  Instead 
of  to  mark  time.  It  is  necessary  to  Introduce  the  standard 
of   difference   Into   our   thought.     Only   by   so  doing  do  we 
attain  to  that  sharp  differentiation  of  elements,  that  clear 
distinction  of  8  and  P  from  one  another,  which  Is  essential 
to  the  Intellectual  organisation  of  our  experiences.    In  place 
of  the  even  flow  of  sensory  consciousness,  the  buss  and  hum 
of  unreflective  life,  we  now  have,  taken  out  of  the  stream  of 
consciousness,  carved  out  and  separated  off  from  one  another, 
elements  which   have  lost  the  continuity  of  their  sensory 
character,  and  have  become  loosed  from  their  context  and 
Intellectuallsed.  flxed  by  the  mind  negaUvely  as  well  as  posi- 
tively—the differentiated  Identities,  8  and  P.     It  Is  on  the 
distinction,  as  well  as  the  Identity,  that  we  depend  for  the 


58 


DIFFERENCE 


new  combination  of  these  elementa  which  gives  n*  intellectu- 
ally organised  experience,  in  a  word,  empirical  science. 

Here  also,  as  in  the  perceptual  judgment,  we  may  further 
note  that,  as  within  the  Judgment  S  and  P  are  distinguished 
from  one  another,  so  also  t..e  standard  of  difference  distin- 
guishes the  judgments  as  a  whole,  as  an  intellectuallsed  com- 
plex, from  the  sensory  consciousness  out  of  which  it  has  been 
cut  out  and  put  together  by  the  mind. 

(C)  In  Symbolic  Judgments.— Let  us  consider  such  a  judg- 
ment as  "Rome  was  occupied  by  Caesar."  To  form  a  clear 
Idea  of  the  sensory  level  of  the  reading-consciousness,  as  dis- 
tinct from  the  Intellectual  level  of  clear-cut  judgment,  we 
must  call  to  mind  those  states  of  fatigue  or  distraction,  in 
which  our  eye  has  followed  the  symbols  on  the  prints'  page, 
but  our  mind— as  we  eventually  discover— has  not  taken  in 
the  meaning  at  all.  It  is  possible  for  the  eye  to  have  made 
every  adjustment  necessary  for  distinct  vision,  it  is  possible 
for  the  hands  to  have  turned  over  page  after  page  in  due 
course,  and  yet.  when  we  look  back  on  what  we  are  supposed 
to  have  read,  we  discover,  only  too  clearly,  that  our  experi- 
ence has  remained  at  the  sensory  level,  and  that  we  have 
no  grasp  on  the  subject-matter,  no  intellectual  organisation 
of  our  visual  sensations  sufficient  to  give  us  an  understand- 
ing of  this  chapter  In  Roman  History. 

What  happens,  then,  when  we  do  rise  to  the  intellectual 
level,  and  not  merely  attend  to  the  printed  symbols,  but  read 
into  them  the  full  meaning  which  they  will  bear?  As  we 
attend,  e.  g.,  to  the  word  "Rome,"  the  steady  even  flow  of 
consciousness  Is  arrested.  We  look  before  and  after.  We 
pause  and  think.  The  word  we  read  serves  as  a  nucleus  for 
associations  from  our  past  experience.  As  we  continue  to 
attend,  and  think  of  Rome  as  "occupied  by  Caesar,"  we  split 
up  still  further  the  massive  stream  of  consciousness,  sensory 
and  associative.  We  analyse  It  out  Into  minute  elements, 
and  select  from  our  variegated  experiences  only  such  elements 
of  panic  and  triumph  as  are  suitable  to  the  occasion.  We 
exclude  all  which  are  irrelevant,  different  from  what  we  are 
seeking.  The  concepts  of  "Rome"  and  "occupied  by  Caesar" 
which  we  thus  construct  are  organised  complexes,  into  which 
difference,  as  well  as  identity,  has  entered.  The  elements  out 
of  which  they  have  been  put  together  have  been  carefully 
selected.  In  such  a  way  as  to  exclude  all  which  are  Irrelevant. 


1.    c^J-    <^4/<0-'i 

IN   SYMBOLIC  JUDGMENTS  » 

Inappropriate,  other  than  what  Ib  required.  The  "Rome"  o( 
our  Judgment  Ib  different  from  the  Rome  of  RomuluB,  the 
Rome  of  feclpio  Afrltanus,  the  Rome  of  Sulla.  It  Is  the  Rome 
of  Fompey  and  Caesar,  fartlon-torn  and  fearful  of  proscrip- 
tions. In  short,  Rome  aa  "occupied  by  CneBar."  -  Sc  too  the 
predicate-concept  "occupied  by  Caesar"  la  not  constructed  out 
of  panlc-and-trlumph  elements  In  general,  but  of  such  elem- 
ents torn  from  their  context  In  my  own  experience,  and  ao 
split  up,  altered,  re-orgiinlsed,  that  they  now  repiesent,  not 
my  actual  experience,  but- -something  different,  an  experi- 
ence such  aa  I  might  have  had,  had  I  been  a  citizen  of  Roma 
at  the  time  of  Its  occupation  by  Caesar.  The  sensory  con- 
sdousiiesa  has  thus  become  Intellectuallsed  by  the  Introduc- 
tion of  difference,  as  well  as  Identity. 

A  second  way  In  which  difference  enters  Into  the  Judgment 
is  seen  It  we  consider  the  subject  and  predicate  .conciepts. 
"Rome"  and  "occupied  by  Caesar"  are  contrasted,  set  over 
against  and  opposed  to  one  another.  Each  has  its  own  nature, 
its  own  identity.  But  they  are' diverse  natures,  opposed  Iden-  ■ 
titles,  and  it  is  out  of  the  clash  and  conflict  between  them 
that  the  dramatic  sigulflcance  of  the  Judgment  arises.  A 
mothr  .--city  ought  not  to  be  "occupied"  by  one  of  her  own 
Bone.  It  Is  an  outr  ge,  none  the  less  tragic  becauBe  It  was, 
perhaps.  Inevitable.  «  and  P  are  thus  different,  dietinct.  We 
can,  perhaps  best  realise  the  Importance  of  this  distinction, 
If  we  compare  Ith  the  above  Judgment  auch  statements  ai 
"Rome  is  Rome,  "Caesar  la  Caesar,"  "Occupation  Is  occupa- 
tion." Such  "Identical  propositions "  show  colorless  and  life- 
less in  the  comparison.  If  we  look  atll!  closer,  they  are 
even  meaningless.  If  S  and  P  are  wholly  without  difference, 
if  they  coincide  absolutely  so  as  to  be  one  identity,  and  not 
two,  then  there  is  no  distinction  between  end-point  and  start- 
ing-point of  our  thought:  which  Is  as  much  as  to  say,  there 
has  been  no  act  or  movement  of  thought  at  all.  Nothing  has 
been  accomplished,  no  problem  has  been  solved,  no  meaning 
read  Into  our  sensations.  In  other  words,  difference  Is  essen- 
tial to  the  symbolic  Judgment,  and  its  function  is,  to  spilt  up 
the  stream  of  stnsory  consciousness  Into  sharply  differenti- 
ated element",  out  nf  which  clear-cut.  cleanly  outlined  com- 
plexes,  8  and  P,  can  be  constructed  and  set  over  against  each 


»Cf.  UitzH.  Logic,  seo.  ".8  (E.  T..  p.  «3b). 


60 


DIFFERENCE 


other  In  such  a  way  as  to  produce  meaninct  ttcniflcance, 
intellectual  life. 

Finally,  as  in  the  preceding  types  of  Judgment,  so  here, 
we  may  note  ttiat  dttference  enters  not  only  into  ttie  elements 
out  of  which  8  or  P  is  constructed,  not  only  into  li  and  P  as 
wholeH  contrasted  with  one  another  in  the  judgment,  but 
into  the  judgment  ab  a  whole.  As  an  Intellectuallsed  com- 
plex, this  judgment  can  not  be  too  sharply  dttrerentiated  from 
the  even-flowing  sensory  consciousness  out  of  which  it  has 
l>een  constructed. 

(D)  In  Tranacendent  Judgments. — Take  such  a  judgment 
as  "Qod  is  a  substance  with  infinite  attributes".  Transcen- 
dent judgments  of  this  type  are  so  far  removed  from  the 
sensory  level  of  consciousness,  that  it  is  difllcult  to  determine 
with  certainty  the  sensory  background,  and  especially'  the 
particular  sensory  stimulus  which  induces  us  to  dare  the 
great  venture,  and  seek  a  firm  foothold  for  our  faith  beyond 
the  possibllitieB  of  human  experience.  But.  since  any  stimulus 
whatever  may  lead  to  pursue  a  train  of  reasoning  beyond  the 
bounds  of  experience,  we  may  suppose  something  of  the  fol- 
lowing kind.  We  are  in  a  "brown  study,"  with  a  tendency 
in  the  direction  of  religious  feeling.  The  most  prominent 
factor  in  consciousness  is  simply  vague  feeling,  at  the  undif- 
ferentiated sensory  level.  This  feeling  extends  vaguely,  i.  e., 
without  precise  limits,  over  the  wholt  background  of  experi- 
ence, and  thus,  as  being  without  clear-cut  limits,  presents  a 
kind  of  sensory  analogon  to  infinity.  If  now  the  thought  of 
some  personal  failure,  for  example,  or  the  loss  of  a  loved 
friend,  leads  us  to  think  of  our  own  helplessness,  the  aspira- 
tion after  something  better,  finer,  greater,  less  limited  than 
ourselves  arises  as  a  correlative  idea,  and  as  we  follow  up 
this  line  of  thought,  we  can  hardly  fail  to  pass  beyond  the 
bounds  of  space  and  time,  beyond  the  border-line  which 
separates  the  humanly  possible  from  what  we  can  never 
experience — to  the  idea  of  an  absolutely  perfect.  Ideal,  Divine 
Being,  in  Whom  we  live  and  move,  and  from  Whose  view- 
point all  our  finite,  human  problems  find  their  completely 
satisfying  solution.  This  is  the  thought  of  God,  and  we  have 
reached  it  by  introducing  a  distinction  between  our  own 
imperfect  selves  and  a  perfect,  ideal  self.  It  is  thus  a  complex 
construction  into  whose  organisation  difference,  as  well  as 
identity,  has  largely  entered.    Though  at  this  level  of  thought 


f^vni^ 


IN  TRANSCENDENT  JUDGMENTS^ 


« 


seniory  feellnc.  perhaim.  itlU  playi  a  sreat  part,  It  is  fMllng 
orgatkiKd  arouud  the  thought!  of  (1)  human  Mif,  (S)  Dlvlna 
Self,  and  (3)  the  vaat  difference,  or  rather  ImpaiMble  gulf, 
between  them. 

From  an  Intellectual  feeling  of  this  kind  to  tha  Judgment 
that  Ood  (aa  experienced  in  this  way)  la  a  "auhatanca  with 
Inflnite  attributes,"  ia  perhaps  a  far  cry  for  one  who  may  not 
have  been  educated  Sn  the  technicalities  of  Aristotelian  or 
Splaozistic  terminology.  We  do  not,  perhaps,  quite  naturally 
Interpret  our  feeling  after  au  ideal  Self  in  terma  of  "aub- 
stance"  and  "attributes "  The  terms  are  unfamiliar  to  us. 
But  the  thought  behind  this  terminology,  the  Idea  which 
expresses  itself  In  this  kind  of  way,  is  familiar  enough,  and 
for  our  present  purpose  it  is  suflScient  to  note  that  auch  an 
idea  as  "substance  with  inflnite  attributes"  is  a  complex  idea 
into  which  difference  largely  enters.  There  is  (1)  the  dia* 
Unction  between  substance  and  attribute,  (2)  the  difference 
between  the  many  distinct  attributes  united  in  this  one  Inflnita 
substance,  and  (3)  the  vast  difference  between  these  attrib- 
utes as  we  human  beings  know  some  of  them,  and  these  att.i1>- 
utes  aa  extended  to  infinity,  as  they  are  ascribed  to  Divinity. 

Thus  we  see  that,  as  in  the  symbolic  Judgment,  so  hara, 
both  subject-term  and  predicate-term  ere  complezea  into 
whose  organisation  difference,  as  well  aa  identity,  largely 
enters.  The  fact  that  in  symbolic  Judgment  we  remain  within 
the  field  of  poasible  experience,  whereas  in  transcendent  Judg- 
ment we  pass  beyond  this  to  absolute  infinity,  does  not  seem 
to  involve  anything  new  in  respect  to  the  standard  of  differ- 
ence; for  example,  it  does  not  Involve  our  not  Introducing 
this  standaid.  On  the  contrary,  the  intellectual  element  of 
difference  aeems  to  be  introduced  more  sharply,  in  proportion 
as  our  thought  travels  further  and  further  away  from  direct 
sensory  experience.  Within  the  field  of  experience,  for 
instance,  all  differences  are  merely  relative,  and  it  la  fre- 
quently possible  for  us  to  learn  to  pass  over  the  Intervening 
distances.  But  between  Human  and  Divine,  between  finite 
and  infinite,  between  relative  and  absolute,  there  is  no  ratio. 
Here  the  difference  is  such  that  we  human  beings  can  never 
learn  to  pass  it.  In  fact,  the  whole  point  of  the  transcen-^^ 
dent  Judgment  is  that  It  deals  with  extreme  differencea.  with  ^ 
difference  made  absolute. 

It  remains  to  notice  another  way  in  which  difference  entora 


62 


DIFFERENCE 


'nto  the  transcendent  Judgment.  Not  only  does  difference 
enter  Into  the  organisation  of  elements  which  constitutes  '^rt 
complex  S  or  the  complex  P,  but  S  and  P  as  wholes,  as  u 
are  different  from  one  another.  Both  "God"  and  "substp 
wfth  infinite  attributes"  may,  it  is  true,  be  ways  of  nam»  n 
that  feeling  after  a  perfect  Self  which  we  have  briefly 
described  above.  But  they  are  different  ways  of  describing 
that  experience,  and  we  must  try  to  realise  the  importance 
of  this  difference  for  the  transcendent  judgment.  Consider, 
for  instance,  such  a  statement  as  "God  is  God,"  or  "St'bstance 
is  substance,"  or  "Infinite  attributes  are  infinite  attributes." 
We  see  at  once  that,  by  comparison  with  "God  is  an  infinite 
substance,"  such  "identical  propositions"  (as  tney  are  called) 
are  relatively  colorless,  and  almost  without  meaning.  In 
fact,  if  S  and  P  are  really  intended  in  precisely  the  same 
sense,  if  there  is  no  change  or  development  of  meaning,  then 
no  operation  of  thought  has  taken  place,  nothing  has  been 
Judged.  Difference  between  S  and  P  is,  then,  vital  to  our 
transcendent  thought,  and  serves  to  make  possible  that  move 
ment  and  development  in  our  thinking,  in  which  something 
(P)  is  definitely  judged  of  something  else  (8). 

Finally,  yet  another  way  in  which  difference  enters  Into  our 
transcendent  thinking  is  seen  when  we  compare,  not  S  with 
P.  but  the  Judgment  as  a  whole  with  the  feeling-conscious- 
ness at  the  sensory  level,  from  which  our  clearly  articulated 
thought  that  "God  is  a  substance  with  infinite  attributes"  has 
arisen.  In  place  of  the  steady,  even  flow  of  this  sensory  con- 
sciousness we  have  elements  torn  out  of  their  sensory  contexts 
and  piaced  together  in  a  new  order,  in  such  a  way  as  to  con- 
tribute to  that  highly  articulated  organisation  of  intellect- 
ualised  elements  which  aims  not  merely  at  summing  up  actual 
experience,  or  to  express  symbolically  the  meaning-values  of 
an  experience  thought  of  as  only  possible — but  which  seeks  to 
sum  up  and  state  the  meaning  of  an  experience  which  goes 
infinitely  beyond  what  is  possible  for  human  beings,  and 
transcends  the  range  even  of  what  we  can  clearly  and  con- 
sistently symbolise. 

Thus  we  see  that  the  function  of  difference  In  the  trans- 
cendent Judgment  is,  to  split  up  the  sensory  consciousness 
into  intellectualised  elements,  on  the  basis  of  which  a  complex 
8  and  a  complex  P.  sharply  distinguished  from  one  another, 
are  constructed,  in  such  a  way  as  to  produce  a  single,  highly 


FUNCTION  OF  DIFFERENCE 


63 


organised  Judgment.  This  Judgment,  in  its  turn,  is  clear-cut, 
sliarply  outlined,  and  very  different  from  the  relatively  unor- 
ganiBed  mass  of  sensory  feeling  from  which  it  originated. 
Each  step  of  this  construction  is  a  function  of  difference  no 
less  than  identity,  and,  so  far  as  the  transcendent  differs  from 
the  symbolic  Judgment,  so  much  the  more  strictly  and  rigidly 
has  the  standard  of  difference  been  introduced. 

Conclusion — The  Function  of  Difference. — If  we  put  together 
the  results  reached  in  considering  each  of  the  above  types 
of  Judgment,  we  find  that  the  introduction  of  difference  into 
our  thought  splits  up  the  even-flowing,  continuous  sensory 
stream  into  intellectualised  entities.  Out  of  these,  by  a  proc- 
ess of  selection  and  re-arrangement,  the  intellectually  organ- 
ised complexes,  8  and  P,  are  constructed,  in  such  a  way  as 
to  produce  a  significant  Judgment.  Difference  thus  enters 
into  Judgment  in  three  ways:  (1)  The  elements  out  of 
which  the  complex  S  and  the  complex  P  are  constructed,  are 
sharply  differentiated  from  one  another;  (2)  £1  and  P  as  wholes 
are  clearly  outlined  and  de  mited  against  each  other;  (3) 
finally,  the  Judgment  as  a  whole  is  distinct  from  the  sensory 
consciousness  from  which  it  has  arisen.  Without  difference 
at  each  of  these  stages,  there  would  be  nr  distinctness  in  our 
thought,  and  if  there  were  no  distinctness  in  our  thought,  that 
intellectual  organisation  of  sensory  consciousness  in  which 
Judgment  consists,  could  not  come  into  being. 

In  the  last  chapter,  we  observed  that  the  introduction  of 
the  standard  of  identity  made  itself  noticeable  in  precisely 
these  same  three  ways.  What,  then,  is  new  in  the  present 
chapter?  What  is  new  is  chiefly  another  kind  of  emphasis.  The 
elements  out  of  which  8  and  P  are  constructed  are  identities; 
8  and  P  are  themselves  identities;  and  finally  the  Judgment 
itself,  whether  sensory,  experiential,  symbolic,  or  transcen- 
dent, is  an  identity.  This  represents  a  positive  aspect  of  that 
intellectual  organisation  which  gives  us  Juc'gment.  ^n  the 
present  chapter,  we  have  been  emphasising  a  more  negative 
aspect  of  the  same  mental  operation.  The  identity  which  is 
8  and  the  identity  which  is  P  are  distinct  identitiea,  held 
over  against  and  contrasted  with  each  other  in  one  act  of 
thought:  and  it  is  on  this  difference,  as  well  as  on  identity, 
that  the  significance  of  Judgment  depends.  Similarly,  if  the 
different  elements  out  of  which  8  and  P  have  been  constructed 
were  not  sharply  distinguished,  we  should  have  no  clear-cut, 


64 


DIFFERENCE 


diitinctly  apprehended,  iotellectualised  complexes,  but  merely 
vague  massea  of  sensory  consciousness.  Finally,  if  the  identity 
which  is  the  Judgment  as  a  whole  were  not  very  different 
from  the  relatively  unorganised  sensory  consciousness,  if  it 
were  not  an  articulated  whole  in  which  difference,  as  well 
as  identity,  played  a  large  part,  it  would  not  be  what  we  call 
a  judgment.  From  this  we  conclude  that  identity  and  differ- 
ence are  two  correlative  aspects  of  one  and  the  same  process. 
We  can  only  differentiate  entities  which  have  natures  of  their 
own,  such  as  the  electric  bulb  and  the  typewriter;  and  sim- 
ilarly, if  we  are  to  apprehend  clearly  the  identical  nature  of 
anything,  we  can  do  so  only  by  at  the  same  time  distinguish- 
ing It  from  otht  :  identities  which  It  is  not.  What,  then,  is 
this  process,  of  which  Identity  and  difference  are  two  correla- 
tive aspects?  The  answer  to  this  question  must  be  left  to 
the  following  chapters 

FOR  FURTIIBR  READING 

B.  BoBaoquet,  Logic,  Vol.  II,  pp.  •J08-210.  F.  H.  Bradley.  Princtplet 
of  Loffic.  pp.  1.1.V-142.  B.  Brdmann.  Loffik,  (2nd  Fxllt.).  pp.  247-288. 
W.  Wundt,  Logik.  (3rd  Edit),  pp.  553-55B. 


EXERCISES 

1.  llow  far  doPB  the  standard  of  dlffereiK-e  onter  Into  the  follow- 
iag:  Here  we  are.  This  typewriter  U  heavier  than  that.  I  am 
thlr»ty? 

2.  How  far  does  the  standard  of  difference  enter  Into  the  follow- 
ing: Nobody  love*  me — everybody  hatea  me.  There  la  aaually  an 
enormous  difference  between  a  freshman  and  a  senior.  Radtrties  tand 
to  do  well  In  spring? 

3.  How  does  the  standard  of  difference  enter  Into  the  following: 
A  BfralKht  line  1«  the  shortest  distanre  between  two  points.  Little 
Jack  Horner  sat  In  a  corner.  I  can  do  tomorrow  what  I  am  leaving 
unfinished  today? 

4.  How  does  the  standard  of  difference  enter  Into  th«  following : 
We  ought  to  devotft  our  lives  to  the  service  of  the  highest  ideals.  God 
loves  us.     Our  love  can  never  die? 


CHAPTBR  VII. 


ORGANISATION,  (a)  INTERNAL 


The  Meaning  of  Organisation. — Perhaps  we  can  best  under- 
stand what  Is  meant  by  organisation,  if  we  compare  an  WLggn- 
gate  with  a  totality.  A  chance  heap  of  stones  is  an  aggregate, 
a  juxtaposition  without  Inner  principle,  without  coherence, 
without  unity.  Each  stone  in  such  a  heap  preserves  its  own 
individuality,  and  does  not  unite  with  the  others  in  realising 
some  common  purpose.  On  the  other  hand,  imagine  suitable 
stones  withdrawn  from  the  heap  and  put  together  in  such  a 
way  as  to  construct  an  arch-way  over  a  door.  Such  an  arch- 
way is  a  totality,  and  possesses  a  larger  individuality  of  its 
own.  If  one  of  the  stones  is  withdrawn  the  arch  is  weakened, 
and,  on  the  other  hand,  by  belonging  to  such  a  totality,  each 
;,tone  partakes  in  a  higher  individuality  than  it  possessed  by 
itself,  an  individuality,  e.  g.,  with  social  and  aesthetic,  as  well 
as  physical,  values.  An  organised  totality  Is  thus  a  system- 
atic complex  of  elements,  each  of  which  has  its  own  identity, 
and  is  different  from  each  of  its  fellow-elements;  but  the 
differences  are  not  absolute,  they  are  transcended  so  far  as  all 
elements  are  pervaded  by  one  and  th''  same  common  purpose 
or  meaning,  some  principle  which  unites  them  ail  in  the 
service  of  the  whole,  and  thus  gives  them  a  value  different 
from,  and  higher  than,  that  which  they  possessed  apart  from 
such  organisation. 

I..et  us  apply  this  to  Judgment.  Take  the  case  s3 — y^  s: 
(x  rV)  (x — y).  This  is  a  complex  totality,  a  unity  of  ele- 
ments such  that  if  one  were  withdrawn  or  altered,  the  equation 
would  l>e  radically  changed.  Exchange,  for  Instance,  a  plus  for 
a  minus  sign,  remove  a  pair  of  brackets  or  the  sign  of  squar- 
ing,  and  the  equation  simply  vanishes.  Consider  further  the 
elements  x  and  y.  Apart  from  its  place  in  such  a  Judgment,  x. 
Tor  instance,  has  perhaps,  an  individuality  of  its  own,  as  a  let- 
ter of  the  alphabet,  which  may  conceivably  be  used  as  an  alge- 
braical symbol.  Place  It  In  the  Judgment,  and  it  is  at  once 
altered  by  the  fringe  of  relations  into  which  it  enters.    Theae 

65 


66 


INTERNAL  ORGANISATION 


give  it  a  new  meaning  and  value.  On  the  one  side  of  the 
equation  it  is  squared,  and  i/s  is  subtracted  from  it;  on  the 
other  side,  y  is  added  to  it  in  one  bracltet,  and  subtracted  from 
it  in  another,  and  the  complex  results  are  multiplied  together. 
Further,  both  sides  of  the  equation  have  a  certain  unity:  by 
diverse  paths  they  both  lead  to  one  and  the  same  result.  Our 
element  has  thus  ceased  to  be  the  mere  alphabetical  x,  and  has 
become  a  symbol  transferred  to  do  algebraic  service,  and 
transmuted  in  the  process.  It  is  now  steeped  in  a  new  color- 
ing derived  from  its  relations  to  y  within  the  totality  which 
is  the  whole  Judgment  of  equality.  Furthermore,  while  x  by 
itself  is  different  from  y  by  itself,  the  unity  which  is  the  total 
Judgment  overcomes  and  is  constituted  by  the  special  differ- 
ences of  X  and  y  in  relation  to  one  another  within  the  equa- 
tion. 

So  much  for  a  general  example.  Let  us  now  turn  to  the 
special  types  of  judgment,  in  order  to  consider  the  part  played 
by  organisation  somewhat  more  in  detail. 

(A)  In  Judgments  of  Perception. — Such  a  Judgment  as  "This 
room  is  warm"  is  a  complex  totality  in  which  no  part  could 
be  altered  without  changing  the  meaning.  Let  us  consider 
the  elements  out  of  which  it  is  constructed.  As  for  8  and  P, 
we  have  already  seen  that  "The  room"  and  "warm"  are  iden- 
tities, and  that  they  are  different  Identities.  It  remains  to 
see  how  they  are  organised  with  reference  to  one  another, 
how  the  differences  are  overcome,  and  how,  within  the  Judg- 
ment, both  "The  room"  and  "warm"  acquire  new  and  higher 
shades  of  meaning  by  uniting  to  constitute  the  higher  indi- 
viduality which  is  the  total  Judgment.  Consider  "The  room" 
apart  from  the  judgment.  It  is  a  space  enclosed  by  four  walls, 
a  ceiling,  and  a  floor,  and  possesses  two  windows  and  a  door. 
It  might  be  thought  of  as  usable  for  studying,  or  for  enter- 
taining friends,  or  for  a  thousand  other  purposes.  That  is 
to  say.  it  might  enter  into  u  thousand  Judgments.  But  apart 
from  Judgments  of  definite  kinds,  it  is  not  so  thought  of.  It 
is  merely  "This  room."  Within  the  Judgment  it  at  once 
receives  a  new  meaning.  It  is  thought  of  as  "warm,"  i.  e., 
in  relation  to  temperature-values  as  sensed  by  me,  tempera- 
ture-values of  which,  perhaps,  I  disapprove,  and  which  it  is 
in  my  power  to  alter.  Similarly  "warm"  is  not  thought  of  as 
wa:  ,^h-in-general,  mere  physical  warmth,  but  as  the  genial 
or  unpleasant  warmth  of  this  room  of  mine,  a  degree  of  tem- 


IN  PKRCKPTUAL  JUDGMENTS 


67 


perature  which  may  make  my  work  comfortable  or  uncom- 
fortable, may  leave  me  contented,  or  may  lead  me  to  take 
measures  to  change  the  temperature.  It  is  plain,  then,  that 
in  the  Judgment,  both  "The  room"  and  "warm"  have  become 
pervaded  with  new  shades  of  meaning.  8  is  more  than  mere 
S,  and  P  is  more  than  mere  P.  They  are  now  the  S  and  P 
thought  of  in  relation  to  one  another  in  a  special  Judgment 
which  I  make.  The  organisation  of  £1  and  P  which  is  the 
judgment,  on  the  one  hand  gives  them  their  new  meaning.  On 
the  other,  the  relations  of  identity  and  difference  of  8  and  P 
within  the  new  totality  constitute  my  Judgment  of  perception. 

Let  us  push  our  analyslt*  more  into  detail,  and  examine 
further  the  elements  which  compose  8.  For  8,  within  the 
judgment,  is  itself  no  bare  identity,  but  is  a  complex,  con- 
structed out  of  a  number  of  different  identities.  What,  then, 
are  these  elements?  Let  us  consider.  In  such  a  Judgment  as 
"This  room  is  x  feet  long,  y  feet  broad,  and  z  feet  high," 
"The  room,"  as  the  subject-concept,  is  constructed  out  of  ai«- 
tlal  elements.  In  such  a  Judgment,  on  the  other  hand,  as 
"This  room  is  thoroughly  suitable  for  entertaining  friends,"  the 
1  ubject-concept  is  constructed  out  of  social  elements,  or  at  least 
out  of  elements  which  have  an  especially  social  reference. 
In  the  Judgment  that  "This  room  is  warm,"  again,  it  is  con- 
structed chiefly  out  of  temperature-elements.  In  other  words, 
that  which  decides  Just  which  out  of  the  countless  possible 
elements  shall  be  utilised  in  constructing  8,  is  the  meaning  of 
the  Judgment  as  a  whole.  Is  the  judgment  concerned  with 
spatial  values?  Then  the  S-elements  are  spatial.  Is  it  with 
temperature-values  that  we  have  to  do?  Then  it  is  tempera- 
ture-elements which  constitute  the  main  feature  of  8. 

Similarly  of  the  elements  which  compose  the  predicate. 
Apart  from  the  judgment,  "warm"  is  usually  understood  as 
a  sensation  consequent  upon  the  rapid  motion  of  physical 
particles.  The  concept  "warm."  can  thus  be  built  up  out  of 
motion-elements.  But  in  such  a  judgment  as  "It  is  warm  at 
noon,"  time-elements  enter  into  the  concept;  and  in  such  a 
Judgment  as  "The  bath  is  warm,"  elements  connected  with 
water,  with  washing,  etc.,  enter  in.  In  different  Judgments, 
then,  our  predicate-concept  is  constructed  differently.  We  have 
noondoy-warmth,  bath-warmth,  this-room-w&rmth.  Just  pre- 
cisely which,  out  of  the  Innumerable  possible  elements,  shall 
be  used  in  constructing  our  predicate-concept,  is  thus  seen  to 


tt 


INTERNAL  ORGANISATION 


depeod  upon  tbe  meaning  of  the  Judgment  as  a  whole.  In  thli 
way  we  come  to  realise  that  the  Judgment  as  a  whole,  as  an 
organisation,  is  penetrated  with  one  and  the  same  general 
meaning,  through  and  through,  down  to  the  minutest  details. 
Not  only  8  and  P  as  wholes,  but  also  the  elements  out  of  which 
8  and  P  are  constructed,  are  organised  in  accordance  with  the 
principle  which  gives  us  a  single  Judgment,  an  act  of  thought 
which  is  one. 

It  remains  to  compare  the  sensory  consciousness  with  what 
we  find  when  our  thought  is  organised  so  as  to  reach  the 
intellectual  level.  At  the  sensory  level,  as  we  have  already 
seen,  there  is  a  continuous  flow  of  consciousness,  without 
distinction  or  unity,  not  in  any  way  cut  into  lengths.  Ele- 
ments are  placed  in  this  stream  in  the  chance  order  in  which 
they  happen  to  us,  without  any  reference  to  relevance  or  con- 
gruity.  Thus,  if  we  arbitrarily  cut  off  a  section  of  this  stream 
and  examine  It,  we  find,  e.  p.,  desires  for  something  to  eat, 
a  wish  that  it  were  not  so  cold,  a  half-stifled  suggestion  of 
conscience  that  we  ought  to  be  worlcing,  some  reverberations 
in  consciousness  of  the  last  book  we  have  been  reading,  and 
a  thousand  other  heterogeneous  elements  of  experience,  all 
jumbled  up  together  In  what,  for  the  intellectual  Judgment, 
would  be  hopeless  confusion.  At  tbe  sensory  level,  however, 
this  is  appreciated  only  as  a  vague  richness  of  life-feeling. 
When  this  mass  of  sensory  feeling  is  Intel lectualised,  organ- 
isation, with  its  tools  of  identity  and  difference,  has  analysed 
out  of  the  mass  only  such  elements  as  fit  in  with  the  plan 
of  tbe  Judgment,  has  excluded  every  el<  ment  which  fails  to 
cohere  in  a  single  complex  meaning,  and  leaves  us  with  a 
closely  organised,  coherent  system  of  intellectualised  elements, 
each  of  which  is  permeated  with  one  thought,  and  contributes 
to  the  construction  of  a  complex  thought-totality,  a  Judgment 
which  is  not  many,  but  oneA 

(B)  In  Judgments  of  Experience. — Such  a  judgment  as 
"The  freight-train  disturbances  are  growing  more  troublesome 
every  year"  is  a  complex  totality,  in  which,  if  any  element 
were  omitted  or  added,  some  change  to  the  whole  would  cer- 


1  In  the  above  onne.  and  throuKhdiit  th)>  chapter,  we  are  as'iumlnK 
that  the  Intellectual  proreiw  of  nrxaniiiatlon  Is  <'arrle<l  out  completelv, 
and  thus  reallv  does  |>enetrate  down  to  the  detallH.  In  actual  fact,  in 
the  ni»h  and  nurry  <»f  practical  life.  It  Ix  Heldom  that  we  have  time 
for  Buch  patl«nt  analysln.  and  the  deta'llfi  tend  to  Im>  nlurred  over,  to 
an  extent  wbdch  frequently  leadH  us  Into  sertoiiK  error. 


IN  EXPERIENTIAL  JUDGMENTS 


69 


tainly  result.  Let  ui  consider  the  elements  which  conitltuta 
this  complex,  in  order  to  discover  what  new  increments  of 
meaning,  if  any,  they  acquire  by  entering  into  the  Judgment 
S  in  this  Judgment  is  "the  freight-train  disturbances."  Apart 
from  the  Judgment  this  might  be  used  in  summing  up  imper- 
sonal, neutral  occurrences,  a  fit  subject,  e.  g.,  for  statistics. 
But  the  moment  such  a  subject  enters  into  the  Judgment,  the 
moment  that  such  "disturbances"  are  disturbances  of  my 
work,  and  not  only  so,  but  are  growing  worae,  so  that  I  decide 
that  something  will  really  have  to  be  done— S  has  ceased  to  be 
an  impersonal,  neutral  entity,  and  has  acquired  new  shades  of 
meaning  of  a  very  pronounced  kind.  Similarly  with  P.  Within 
the  Judgment,  P  is  no  increasing-troublesomeness-in-general 
but  is  a  very  specific  kind  of  increasing  troublesomeness.  a 
Ireight-train  troublesomeness  which  interferes  with  my  work 
to  such  an  extent  that  I  am  goaded  into  action.  8  Is  no  mere 
subject,  but  the  subject-of-this-predlcate:  and  P  is  no  mere 
predicate,  but  the  predicate-of-this-subject.  Apart  from  the 
experiential  Judgment  which  brings  them  together  in  thii 
way,  each  would,  no  doubt,  possess  its  own  individuality,  but 
they  would  not  enter  into  that  larger  Individuality  of  the 
judgment,  in  which  they  participate  in  a  wider  and  deeper 
signiflcance.  and  constitute  integral  portions  of  a  meaningful 
thought-structure. 

I^t  us  now  consider  8  and  P.  not  so  much  iu  their  relation 
to  the  total  Judgment,  as  in  their  character  as  complexes.  For 
the  experiential  Judgment  is  a  summing  up  of  many  more 
elementary  perceptual  experiences,  and  this  characteristic  of 
(omplexlty  is  reflected  in  the  constitution  of  8  and  P.  In  the 
case  of  8,  It  is  not  difficult  to  realise  what  elementary  percep 
tual  experiences  are  therein  summed  up:  the  elements  are 
olearly  single  sense-experiences  of  freight-train  disturbances. 
lust  what  principle  governs  the  selection  of  these  experi- 
ences, we  can,  perhaps,  best  realise  by  comparing  a  number 
of  judgments  with  the  same  subject.  (1)  "The  freight-train 
disturbances  are,  on  the  whole,  a  help,  a  stimulus  to  better 
work";  (2)  "The  freight-train  disturbances  are  things  of  the 
past,"  (3)  "The  freight-train  disturbances  are  amply  com- 
l<«nsated  for  by  the  ease  with  which  we  send  and  receive  ship- 
ments." In  each  of  these  cases,  8  is  the  disturbance  of  my 
work  due  to  freight-trains.  But  in  each  case  It  is  composed 
of  slightly  different  elements,  and  has  a  distinctly  different 


90 


INTERNAL  ORGANISATION 


coloring.  In  the  flrst  rase,  the  dUturbanre  ti  looked  on,  not 
at  a  blank  evil,  which  must  be  atopped,  but  as  a  positive  help, 
a  "most  favorable  pause,"  as  the  psychologists  call  It.  8  is 
in  this  case  a  complex  composed  of  a  series  of  "most  favor- 
able pauses."  In  the  second  case,  the  disturbances  to  my  work 
are  over  and  done  with,  things  of  the  past,  out  of  practical 
politics  once  for  all.  The  elements  of  which  8  is  composed  are 
here  single  disturbances,  to  each  of  which  is  appended  the 
clearly  written  label,  Past-and-done-with."  In  the  third  case, 
the  disturbances  to  my  work  are  real  enough,  but  the  advan- 
tage of  having  my  shipments  carried  is  so  much  in  the  fore- 
ground of  my  consciousness,  that  I  am  willing  to  put  up  with 
a  little  disturbance.  In  this  case,  the  complex  £1  Is  composed 
of  a  number  of  freight-train  noises,  each  of  which  has  two 
sides,  (a)  a  disturbing  side,  (b)  an  advantageous  side  which 
at  least  counterbalances  the  disturbance.  In  the  case  which 
we  are  especially  considering,  8  is  composed  of  a  number  of 
single  train-disturbances,  which  are  thought  of  as  without 
redeeming  qualities,  as  troublesome,  and  Increasingly  trouble- 
some, as  goading  me  into  action  of  some  sort.  On  what  does 
the  difference  in  the  composition  of  8  depend.  In  these  vari- 
ous cases?  It  is  not  hard,  after  such  comparison,  to  realise 
that  it  depends  on  the  Judgment  as  a  whole.  In  making  a 
Judgment  with  an  eye  to  "favorable  pause."  we  select  from 
the  mass  of  experiences  only  such  as  are  thoroughly  attuned 
to  this  chord,  and  can  be  regarded  strictly  from  that  view- 
point. In  making  a  Judgment  in  the  light  of  irritated  feelings 
of  Increasing  troublesomeness,  we  naturally  pick  out  for  our 
complex  8,  only  such  elements  as  are  to  the  point,  strictly 
relevant  to  the  Issue.  In  the  same  way,  the  elements  out  of 
which  P  is  constructed  depend  on  the  principle  of  organisa- 
tion which  gives  us  the  Judgment.  Consider  the  following 
cases:  ( 1 )  "My  increasing  correspondence  is  growing  more 
troublesome";  (2)  "The  management  of  my  increasing  Income 
is  growing  more  troublesome";  (3)  "To  have  so  many  atten- 
tive and  devoted  friends  is  growing  more  troublesome."  We 
can  see  at  once  that  the  elements  out  of  which  the  "trouble- 
someness" Is  constructed,  must  be  distinct  in  such  cases  as 
correspondence,  management  of  income,  and  numerous 
friends.  In  fact,  without  further  analysis  we  can,  perliaps, 
sufficiently  realise  that  the  difference  in  coloring  which  thus 
spreads  over   the   elements  out  of   which  P  is  constructed. 


IN  EXPERIENTIAL  JUDGMENTS 


n 


comet  from  the  Judgment  as  a  whole.  In  thU  way  we  aee 
that,  both  in  the  case  of  £1  and  In  the  caee  of  P,  the  new 
coloring,  the  new  shade  of  meaning,  paseei  orer.  transforme, 
and  permeates  every  detail,  In  exact  proportion  as  Che  Judg- 
ment is  thoroughly  organised  on  one  principle. 

We  must  now  compare  the  Judgment  as  organised,  with  the 
sensory  level  of  consciousness.  At  the  sensory  level,  as  we 
have  seen,  our  present  sense  of  the  train-rumble  expands  in 
space  and  time,  so  as  to  include  in  one  continuum  all  similar 
train-rumbles  in  the  past.  But  it  remains  to  point  out  that 
this  continuum  differs  sharply  from  the  intellectual  organi- 
satiod  of  those  same  train-rumble  experiences.  The  sensory 
continuum  contains  these  experiences  in  the  same  order  in 
which  they  first  happened  to  us.  They  are  not  compared  and 
summed  up.  And  further:  they  do  not  stand  out  from  their 
context,  but  each  Is  embedded  in  a  tissue  of  associated  experi- 
ence, which  clings  to  the  rumble-experience  merely  because 
it  occurred  to  us  at  the  same  place,  or  in  immediate  sequence. 
Association  by  contiguity  or  succession,  as  this  is  technically 
called,  is  mechanical,  unintelligent,  blind,  a  matter  of  chance 
happening,  rather  than  of  rational  organisation.  Rational 
organisation  analyses  this  mass  of  associated  experiences, 
selects  only  what  is  appropriate  to  the  purposes  of  the  Judg- 
ment, excludes  everything  which  is  irrelevant,  and  out  of 
elements  thus  chosen  for  their  suitability  constructs  the  com- 
plexes 8  and  P,  in  such  a  way  that  their  relation  to  one 
another  contributes  to  the  unity  and  significance  of  the  Judg- 
ment as  a  whole.  Intellectual  organisation,  then,  penetrates 
down  to  the  minutest  details  of  the  experiential  Judgment, 
and  rearranges  these  in  the  light  of  Its  own  principle,  or 
main  purpose.  Only  thus  do  we  construct  a  complex  thought- 
totality  which  has  unity,  a  Judgment  or  act  of  thought  which 
is  one. 

(C)  In  Symbolic  Judgments. — Take  such  a  Judgment  as 
"Rome  was  occupied  by  Claesar."  That  this  is  a  totality,  a 
complex  which  has  its  own  principle  of  unity,  we  can  at  once 
realise  If  we  try  to  change  any  of  the  component  elements. 
Let  us  consider  these  elements,  and  see  what  new  shades  of 
meaning  they  acquire  by  entering  Into  this  totality.  B  for 
instance,  apart  from  this  Judgment  is  the  city  of  the  seven 
hills,  the  subject  of  the  various  changes  recorded  in  the  His- 
tory of  Rome.     How  this  differs  from   the  "Rome"  of  our 


72 


INTERNAI.  ORGANISATION 


Judgment,  we  can  periwpe  beet  realise  If  we  compare  a  num- 
ber of  JudgmenU,  In  each  of  which  "Rome"  ti  the  subject. 
B.  g.,  (1)  "Rome  Is  the  city  of  the  seven  hills":  (2)  "Rome 
was  the  chief  seat  of  the  medieval  Christian  Popes,"  (3) 
"Rome  is  the  seat  of  the  modern  Italian  government."  In 
none  of  these  cases  do  we  And  any  of  that  eicitement  of  panic 
and  triumph  characteristic  of  the  Rome  occupied  by  Caesar. 
Oeographical  Rome,  Christian  or  Papal  Rome,  the  Italian 
capital — we  at  once  see  that  as  the  Judgments  differ,  into 
which  the  concept  "Rome"  enters,  so  does  the  concept  Itself 
differ.  In  the  case  especially  before  um,  it  is  the  panic  and  tri- 
umph, the  flight  of  Pompey  and  the  in-march  of  Caesar's  vet- 
erans, which  lend  their  shades  of  meaning  to  the  city  of  the 
seven  hills.  By  entering  into  such  a  Judgment,  the  concept 
has  acquired  a  distinctive  meaning,  new  shades  of  significance 
which  it  never  possessed  before.  So  too  of  the  predicate-con- 
cept "Occupied  by  Caesar"  has  a  different  significance  when 
predicated  of  Rome,  than  when  predicated  of  e.  g.,  the  various 
cities  of  Oaul  or  Spain.  These  latter-mentioned  "occupations" 
were,  in  a  way,  legitimate  enough:  incidents  of  minor  impor- 
tance in  wars  sanctioned  by  the  conditions  of  the  age.  But 
the  forcible  occupation  of  Rome  by  one  of  her  own  cltixens 
was  of  major  importance,  a  matter  of  especial  daring,  and — 
in  spite  of  precedent — was  felt  by  many  to  be  without  pos- 
sible Justification.  Thus  we  see  that  "occupied  by  Caesar" 
has  a  different  significance  in  different  Judgments.  In  other 
words,  the  predicate-concept,  as  well  as  the  subject-concept, 
receives  a  new  coloring,  peculiar  shades  of  meaning,  from 
the  Judgment  into  which  it  enters. 

If  we  carry  our  analysis  further,  and  consider  not  merely 
8  and  P  as  wholes,  but  the  elements  out  of  which  8  and  P  are 
made,  here  again  It  is  not  difficult  to  realise  that  these  two 
are  permeated  with  the  meaning  of  the  Judgment  into  which 
they  enter.  In  every  symbolic  Judgment,  as  we  have  seen, 
the  elements  out  of  which  we  construct,  for  example,  our 
fi-concept,  are  drawn  from  our  own  experience,  and  selected 
and  arranged  in  order  to  meet  the  requirements  of  the  spe- 
cial case.  In  Rome  as  the  city  of  the  seven  hills,  the  elements 
from  which  we  construct  the  S-concept  are  experiences  of 
hills,  geographical  experiences.  In  the  second  case,  the  ele- 
ments are  peaceful.  Christian  experiences,  suited  to  the  milder, 
more  religious  and  venerable  aspects  of  Church  history.    In 


*4  \^J^ 


IN  SYMBOLIC  JUDGMENTS 


71 


tb«  third  caM.  it  la  elvmenti  connected  wltb  th«  MplimtioB 
for  liberty  and  unification— aMOclated  wt^h  the  names  of 
Oarlbaldl.  Victor  Immanuel,  and  Humbert  -on  which  we 
draw.  In  the  Rome  occupied  by  Caeaar,  on  the  other  hand, 
it  is.  as  we  have  already  seen,  elements  of  panic  and  triumph, 
which  we  tear  from  their  contexts  in  our  personal  history 
and  reconstruct  in  such  a  way  as  to  feel  something  as  a 
Roman  cltisen  might  have  felt  under  the  circumstances.  That 
is  to  say.  In  selecting  the  elements  out  of  which  to  construct 
our  fi-concept,  we  are  governed  strictly  by  the  Judgment  as  a 
whole,  and  accept  only  such  elements  as  are  relevant  to  the 
general  meaning  of  that  judgment. 

So  too  with  the  elements  out  of  which  P  is  constructed. 
"Occupied  by  Caesar  has,  as  we  have  seen,  different  shades 
of  meaning  in  different  Judgments.  From  our  present  stand* 
point,  this  means  that  the  elements  which  we  take  from  our 
own  experiences  and  re-arrange  so  aa  to  realise  the  meaning 
of  our  concept,  differ  when  the  meaning  Is  different.  When 
•t  is  some  Gallic  town  which  is  occupied  by  Caesar,  we  do 
not  select  feelings  appropriate  to  the  occupation  of  the  great* 
est  city  of  the  then  world,  which  was  at  the  same  time 
Caesar's  own  mother-city.  Thus  we  see  that,  in  every  detail 
of  the  Judgment,  in  the  elements  o(  which  B  and  P  are  made 
up,  as  well  as  in  the  case  of  J8  and  P  taken  as  wholes,  as  unlta. 
the  principle  which  governs  the  selection  of  materials,  and 
decides  what  shall  be  used  and  what  rejected.  Is  the  meaning 
of  the  Judgment  as  a  whole,  the  principle  of  organisation 
which  makes  it  one  complex,  a  totality. 

Finally,  we  must  compare  the  organised  symbolic  Judgment 
with  the  sensory  level  from  which  it  has  arisen,  the  level  at 
which  our  eye  appreciates  the  form  and  position  of  the  let- 
ters, and  our  hand  turns  over  the  pages,  but  our  minds  fall 
to  grasp  and  hold  fast  the  further  meaning  of  the  symlwls 
In  our  printed  book.  At  the  sensory  level,  our  consciousness 
flows  evenly  along,  without  a  ripple  disturbing  the  serenity 
of  its  surface,  blissfully  unaware  of  the  tragedies  of  Roman 
life  and  the  ascendency  of  Caesar's  star.  Intellectual  organ- 1 
isatlon  of  this  stream  of  consciousness  occurs  when  we  arrest 
the  flow  of  this  stream  in  order  to  stop  and  think.  We  look 
before  and  after,  combine  the  letters  into  words,  the  words 
into  the  unity  of  apprehended  sentences,  of  Judgments  in 
which  the  symbols  are  realised  in  terms  of  re-organlsatlons 


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74 


INTERNAL  ORGANISATION 


of  associated  experiences.  It  is  like  what  happens  in  the 
experiential  judgment,  but  with  this  difference,  that  the 
organised  result  represents  no  mere  summing  up  of  our  own 
experiences,  but  goes  further.  It  consists  of  an  organisation 
of  experienced  elements  which  approximate  to,  and  are  used 
to  stand  for,  an  experience  we  have  never  had,  the  experience 
of  a  citizen  of  Rome  during  the  time  of  its  occupation  by 
Caesar.  Our  intellectual  organisation  penetrates  down  to  the 
minutest  elements  of  our  thought,  the  fragmentary  experi- 
ences which  we  put  together  in  order  to  realise  what  is  meant 
by  8  and  P,  and  every  element  In  the  judgment,  so  far  as 
it  is  intellectually  organised,  is  penetrated  through  and 
through  with  one  and  the  same  complex  meaning,  in  such  a 
way  as  to  give  us  an  act  of  thought  which,  though  complex, 
is  single,  a  judgment  which  is  one. 

(D)    In    Transcendent   Judgments.— Such    a   judgment   as 
"God  is  a  substance  with  infinite  attributes"  is  an  organised 
totality,  i.  e.,  is  such  that  if  a  single  element  (e.  g.,  one  of 
the  Divine  attributes)  were  taken  away,  the  meaning  would 
be  radically  altered.     Let  us  consider   these  elements.     As 
belonging  to  an  organised  whole,  they  must  be  altered  by 
participating  in  It.     Consider  8.     Apart  from  the  judgment, 
"God"  might  mean,  e.  g.,  the  ideal  of  a  Perfect  Self  to  which 
we  aspire.    God  as  the  goal  of  aspiration  differs  sharply  from 
God  as  a  "substance  with  infinite  attributes."     The   warm, 
personal  shades  of  meaning  associated  with  human  aspira- 
tion  are   lost   in   the   Impersonal,   mathematical   relation   of 
attributes  so  many  as  to  transcend  all  human  qualities  what- 
ever.    The  concept  of  God  has  now  acquired  the  "eternal" 
or  timeless  aspect  which  we  attribute  to  mathematical  entities, 
and  the  chill  remoteness  of  this  highly  intellectual  fringe  of 
meaning  has  altered  our  concept  almost  beyond  recognition— 
at  least,  for  all  who  have  not  yet  learnt  to  consider  ideas 
suh  specie  aeternitatis.    Similarly  the  predicate-concept  "sub- 
stance  with  infinite  attributes"— in  Itself  a  wholly  colorless 
quasi-mathematical   entity— acquires   by   being  associated   In 
one  and  the  same  act  of  thought  with  "God"— the  object  of 
reverence  and  aspiration— something  at  least  of  the  warmth 
and  Intimacy  of  personal  feeling,  a  shade  of  meaning  which 
connects  it  with  human  life.    Thus  we  see  that  both  8  and  P 
receive  new  and  valuable  elements  of  meaning  by  entering 


IN  TRANSCENDENT  JUDGMENTS 


75 


into  the  intellectual  organisation  which  is  the  transcendent 
judgment. 

Let  US  consider  {-"ther  the  elements  which  together  con- 
stitute the  complex  >^  ind  the  complex  P.  These  elements  are, 
of  course,  selected  as  being  suitable  to  form  £1  and  P.  But  if 
the  standard  of  organisation  has  been  thoroughly  introduced 
into  the  Judgment,  we  should  expect  only  those  elements  to 
have  been  selected  which  are  appropriate  to  the  special  mean- 
ing of  this  iS  and  this  P  in  our  organised  Judgment.  Let  us 
consider  whether  this  is,  in  fact,  the  case  with  8.  Are  the 
elements  which  constitute  the  concept  of  God  the  same  in 
such  Judgments  as  "God  is  the  all-knowing,  all-powerful 
creator  of  the  world,"  "God  is  the  ideal  spiritual  life  in  which 
we  live  and  move  and  have  our  being,"  and  "God  is  a  sub- 
stance with  infinite  attributes?"  A  little  attention  sufBces 
to  convince  us  that  the  component  elements  of  the  God-con- 
cept are  different  in  each  of  these  Judgments.  In  the  first, 
God  is  thought  of  as  composed  of  elements  of  knowledge  and 
power  suitable  to  the  world-creator,  magnificent,  wonderful, 
The  subject  of  admiration  and  perhaps  fear.  In  the  second, 
God  is  thought  of  as  iife  at  its  best,  the  kind  of  life  of  which 
we  catch  faint  glimpses  in  our  most  exalted  moments,  and 
the  component  elements  of  the  concept  are  precisely  these 
moments  of  life  in  which  we  are  at  our  best.  In  the  third, 
the  elements  which  together  constitute  the  concept  are  the 
diHerent  attributes,  extension,  thought,  and  an  infinity  of 
others,  each  one  of  which  is  magnified  to  infinity.  As  far  as  8 
is  concerned,  then,  it  appears  that  its  constituent  elements 
have  been  selected  in  accordance  with  the  meaning  of  the  Judg- 
ment as  a  whole. 

So  too  of  the  elements  which  together  make  up  the  predi- 
cate-concept. Extension  and  thought,  as  attributes  within  our 
human  experience,  are  imperfect  and  finite.  But  as  attrib- 
utes of  a  substance  which  is  not  human  but  Divine,  they 
are  at  once  altered  to  fit  the  new  case.  We  piece  out  their 
Imperfections  with  our  thoughts,  and  try  to  conceive  them 
as  perfect,  or,  as  Spinoza  expresses  it,  "infinite."  Further, 
we  human  beings  know  only  the  two  attributes  of  extension 
and  thought.  But  when  we  wish  to  build  up  the  idea  of  a 
substance  which  is  God,  we  postulate  an  infinity  of  other 
attributes,  of  which  we  have  not  the  faintest  positive  idea, 
but  only  the  persuasion  that  they  must  be  added  as  necessary 


76 


INTERNAL  ORGANISATION 


elements  in  the  absolutely  perfect  Being.  For  this  is  to  be 
without  limitations  or  wants,  and  transcends  the  best  that 
we  human  beings  know,  not  only  in  quality,  but  also  in  quan- 
tity. In  this  way,  then,  we  see  that  the  introduction  of  the 
standard  of  complete  intellectual  organisation  affects  not  only 
the  8  and  P  of  our  transcendent  judgment  considered  as 
wholes,  but  also  the  minutest  details  among  their  component 
elements. 

It  remains  to  compare  the  transcendent  judgment  as  a 
whole  with  the  sensory  consciousness  from  which  it  has 
arisen.  At  the  sensory  level  we  have  a  vague  general  aware- 
ness, without  precise  limits,  which  contains  in  the  germ  the 
feeling  of  helplessness  and  dependence,  as  well  as  countless 
impulses,  sensations,  and  feelings  of  all  sorts.  On  the  limpid 
surface  of  this  broad  stream,  larger  ripples  come  and  go;  but 
they  are  lost  in  the  general  motion  of  the  stream,  and  nowhere 
do  we  find  sharp  outlines,  clear-cut  distinctions.  All  it  con- 
tinuous, even,  placid.  In  comparison  with  this  sensory  level, 
the  introduction  of  organisation  which  results  in  the  trans- 
cendent judgment  stands  out  in  the  greatest  possible  contrast. 
It  is  all  lineb  and  angles,  discontinuities,  sharply  differenti- 
ated identities.  The  stream  of  consciousness  has  been  split 
up  into  innumerable  distinct  elements.  The  hundred  and  one 
elements  which  are  irrelevant  to  the  conception  of  God  as  a 
substance — e.  g.,  the  sensations  and  impulses  arising  from  the 
chance  sounds  and  sights  of  the  external  world — are  sifted 
out  and  excluded  from  the  judgment.  On  the  other  hand, 
all  elements  which  are  strictly  relevant — such  as  feelings  of 
helplessness  and  human  dependence — ^are  retained,  and  not 
merely  retained,  but  retained  in  a  very  special  form.  They 
are  differentiated  and  identified,  cleared  of  every  vestige  of 
irrelevance,  purified  of  the  particular  accidents  of  their  sen- 
sory contexts,  brightly  polished  until  they  are  fit  to  take 
their  place  in  the  new  system — a  system  characterised  by 
intellectual  clearness,  coherence  of  meaning,  unity  of  plan. 
In  place,  then,  of  a  stream  of  sensory  waves  bound  together 
merely  by  the  continuity  of  happening,  we  have  a  system  of 
intellectualised  elements  distinguished  and  held  over  against 
one  another  in  a  unity  which  is  bound  together  by  Identity 
of  reference,  relevance,  meaning. 

Conclution — ^The  Function  of  Organisation. — If  we  now  put 
together  the  results  reached  in  considering  the  various  types 


FUNCTION  OF  ORGANISATION 


77 


of  judgment,  perceptual,  experiential,  symbolic,  and  transcen- 
dent— we  see  that  organisation  makes  itself  felt  by  uniting 
diverse  identities  in  the  service  of  one  common  purpose  or 
meaning.  We  see  this  especially  in  three  ways:  (1)  With 
reference  to  8  and  P.  These  are  diverse  identities.  Apart 
from  the  organisation  which  brings  them  together,  each  has 
its  own  individuality  and  meaning.  But  when  organised, 
with  reference  to  each  other,  in  a  single  act  of  thought,  each 
acquires  a  new  significance  by  partaking  of  a  common  mean- 
ing, which  is  wider  and  deeper  than  either  possessed  by  ttself, 

(2)  The  elements  which  together  make  up  8  and  P  are 
similarly  influenced  and  transformed,  down  to  their  minutest 
details,  by  entering  into  the  organised  Judgment.  According 
to  the  meaning  of  the  judgment,  some  of  the  possible  elements 
are  sifted  out  and  rejected,  while  others  are  taken  up  and 
joined  together  in  the  service  of  the  new  judgment  which 
makes  them  partakers  of  its  own  meaning.  That  is  to  say, 
only  such  elements  are  selected  as  are  suitable  to  form,  not 
S-in-general  or  P-in-general,  but  the  S-in-relation-to-P,  and 
the  P-in-relatlon-to-S,  in  the  unity  of  the  new  act  of  thought. 

(3)  Finally,  by  comparison  with  the  sensory  consciousness, 
we  discover  that,  while  at  ihe  sensory  level  the  different  com- 
ponent elements  of  the  conscious  stream  are  held  together  by 
continuity,  in  the  order  in  which  they  have  happened  to 
U8— at  the  intellectual  level,  the  articulate  system  of  elements 
in  which  the  organised  judgment  consists  is  held  together 
by  identity  of  reference  and  unity  of  meaning. 

FOK  FURTHER  READING 

t 

J.  G.  mbben.  Logic.  Part  1,  chapter  xl.     Chr.  Slgwart,  Logic,  Vol. 

II.  pp.  144-158. 


EXERCISES 

1.  What  are  8,  P,  and  their  respeotlTe  elements,  and  how  are 
they  affected  by  being  brought  together  In  the  following  Judgments: 
These  beets  taste  excellent.  This  overcoat  Is  too  heavy.  That  dark 
patch  is  slippery? 

2.  What  are  8,  P,  and  their  respective  elemeots,  and  how  are  they 
affected  by  being  brought  together  In  the  following  Judgments :  I  have 
found  shorthand  useful  In  my  work.  The  business  section  of  the 
town  has  been  expanding  In  the  last  few  years.  Spinach  has  proved 
unsatisfactory  as  a  garden  vegetable — at  least  In  my  experience. 

8.     What  are  8,  P,  and  their  respective  elements,  and  how  are  they 


78 


INTERNAL  ORGANISATION 


affected  by  being  brougbt  together  In  the  following  Judgments :  Hon- 
esty la  the  be«t  policy.  The  sourcea  upon  which  Tacitus  relied  In 
writing  his  AnnaU  were  prejudiced.  A  life  spent  without  reflection — 
without  taking  stock  of  one's  powers  and  critically  deciding  upon  a 
plan  of  action — ils  no  life  at  all? 

4.  What  are  8,  P,  and  their  respective  elements,  and  how  are 
they  affected  by  being  brought  togetJher  In  the  following  Judgments : 
What  mutt  be,  and  may  be,  assuredly  is.  With  God,  all  things  are 
possible.  I  have  Invented  a  motor  which  will  generate  Its  own  motive 
power,  and  thus  go  on  for  ever. 


CHAPTER  VIII 


ORGANISATION,  (B)   EXTERNAL 


The  Introduction  of  External  Or8«nl»«tlon.— Let  us  con- 
sider what  we  already  know  about  organisation.  The  minut- 
est elements  of  our  thought  are  organised  from  the  viewpoint 
of  some  wider  unity,  which  is  8  or  P.  8  and  P  in  turn  are 
organised  from  the  viewpoint  of  some  wider  unity,  which  Is 
the  judgment.  Can  we  continue,  can  we  regard  Judgments 
also  as  organised  from  the  viewpoint  of  some  yet  wider 
unity?  S  and  P,  for  instance,  have  two  kinds  of  organisa- 
tion. (1)  In  reference  to  their  constituent  elements,  they 
are  internally  organised.  (2)  In  reference  to  the  judgment 
as  a  whole,  they  are  externally  organised.  In  the  same  way, 
the  minutest  elements  are  externally  organised  in  reference 
to  8  and  P,  or  to  the  judgment  as  a  whole.  The  judgment  as 
a  whole,  however,  has  been  so  far  considered  only  in  refer- 
ence to  its  constituent  elements,  i.  e.,  as  Internally  organised. 
In  the  present  chapter  we  must  attempt  to  discover  whether 
it  has  external  organisation  also,  and,  if  so,  what  part  this 
plays  in  our  thought. 

Take,  for  example,  the  judgment  "7+5=12."  This  Is  Inter- 
nally organised  in  reference  to  the  units  which  constitute  the 
judgment.  But  the  matter  does  not  stop  here.  Each  arith- 
metical judgment  is  not  a  unity  with  internal  organisation 
only,  standing,  in  splendid  isolation,  aloof  from  all  other 
judgments.  Arithmetical  judgments  hang  together,  cohere 
in  one  system  of  meaning.  12,  for  instance,  can  be  reached 
by  other  equations,  such  as  20—8,  4X3,  48^4,  etc.,  and  these 
different  judgments  belong  together  in  such  a  way  that  we 
can  say  e.  g.,  "7-f5=20— 8=4X3=48^4=12."  They  belong 
together  in  virtue  of  the  fact  that  they  are  externally  organ- 
ised in  reference  to  one  and  the  same  arithmetical  series,  1, 
2,  3,  ,  .  .  and  represent  the  internal  organisation  of  this 
series.  So  too  geometrical  judgments  cohere  In  one  system, 
being  externally  organised  in  reference  to  space,  plane  geo- 
metry to  a  space  of  two  dimensions,  solid  geometry  to  a 

79 


80 


EXTERNAL  ORGANISATION 


space  of  three  dimensions,  and  "metageometry"  to  a  space  of 
n  ditnensionB.  Similarly  algebraical  Judgments  belong  to 
a  single  system,  and  if  we  pass  to  the  more  empirical  sciences 
of  physics,  chemistry,  biology,  psychology,  etc.,  we  must 
recognise  here  also,  that  each  of  these  sciences  consists  of 
a  group  of  more  or  less  coherent  judgments. 

But  the  matter  does  not  stop  even  here.  These  various 
groups,  arithmetic,  psychology,  physics,  etc.,  are  organised 
still  further  in  reference  to  one  another,  or  perhaps  to  a 
wider  unity  to  which  all  alike  belong.  Many  problems,  for 
instance,  can  be  rolved  Indifferently  by  arithmetic,  algebra, 
or  geometry.  New  discoveries  in  physics  or  chemistry  shed 
light  on  dark  places  in  botany,  psychology,  etc.,  and  all  the 
natural  sciences  make  much  use  of  mathematical  equations. 
This  universal  use  of  mathematics  shows  that  the  various 
scientific  thought-structures  have  at  least  one  common  factor. 
When  we  further  reflect  that  biology,  psychology,  physics, 
etc.,  deal  with  relations  of  cause  and  effect,  while  all  sciences 
whatever  deal  with  relations  of  ground  and  consequent  and 
other  logical  relations — i.  e.,  where  all  sciences  make  use  of 
logic  and  mathematics,  they  must  be,  to  that  extent  at  least, 
interrelated,  must  form  parts  of  a  wider  whole  which  is  at 
least  partially  organised.  From  this  we  can,  perhaps,  realise 
that  all  judgments  whatever  are,  at  least  ideally,  interrelated, 
and  all  belong  to  the  vast  body  of  organised,  or  ideally  organ- 
isable,  knowledge. 

The  ideal  of  knowledge  is  thus  a  vast  system  in  which  all 
possible  discoveries  in  the  departmental  sciences  might  be 
completely  organised  in  reference  to  one  another.  The  system 
is  internally  organised  in  the  form  of  the  special  sciences,  and 
conversely,  the  various  judgments  which  compose  the  special 
sciences  can  be  regarded  as  externally  organised  in  reference 
to  this  system  of  possible  knowledge,  and  thus  as  being  sub- 
ject to  the  demands  of  consistency  within  a  system  which  is 
one.  The  unity  of  the  thinkable  is  thus  the  ultimate  intel- 
lectual principle,  in  reference  to  which  all  judgments  are 
externally  organised,  or  at  least  externally  organisable.  In 
actual  practice,  in  the  hurry  and  rush  of  our  every-day  con- 
cerns, few,  even  scientists,  push  their  researches  to  this  length. 
They  tend  to  remain  content  with  an  external  organisation 
v/hich  merely  gives  the  fringe  or  general  setting  of  their 
special  science;  but  it  is  always  understood  that  such  results 


IN  PERCEPTUAL  JUDGMENTS 


81 


are  provisional  merely,  until  they  hare  been  worked  over 
and  transformed  from  a  deeper  viewpoint.^  Then  only  are 
they  fit  to  take  their  position  ii  the  ideal  system  which  is 
Truth. 

So  far,  then,  we  have  seen  that  Judgments  are  externally 
organised  (a)  in  reference  to  the  special  department  of  knowl- 
edge within  which  they  fall,  and  (b)  in  reference  to  the  ideal 
unity  of  what  can  be  thought  consistently.  Let  us  con- 
sider the  meaning  and  value  of  this  for  the  special  types  of 
judgment. 

(A)  In  Judgment*  of  Perception. — Take  such  a  Judgment 
as  "This  room  is  warm."  In  the  sense  in  which  we  have 
hitherto  understood  it,  this  Judgment  falls  into  at  least  the 
following  departments  of  knowledge:  (1)  temperature-Judg- 
ments, (2)  sense-Judgments,  (3)  practical  Judgments.  (4) 
psycho-physical  Judgments  with  a  background  of  nervous 
physiology,  leading  to  (5)  chemical  and  (6)  physical  Judg^ 
ments,  with  all  which  these,  in  their  turn,  also  imply.  Ulti- 
mately, it  belongs  to  (7)  the  class  of  "thinkables,"  i.  c,  Judg- 
ments intellectually  organised  in  the  systematic  unity  which 
contains  every  possible  thought. 

Let  us  conpider,  then,  for  the  perceptual  Judgment,  what 
is  the  meaning  and  value  of.  its  external  organisation  In 
respect  of  these  various  classes.  For  example,  the  tempera- 
ture class  consists  of  Judgments  like  "This  it  cool,"  "This 
is  warm,"  "This  is  Just  right,"  That  is,  it  is  Internally 
organised  into  a  number  of  precise  Judgments  which,  taken 
together,  contain  the  whole  meaning  of  the  temperature  class. 
If  any  one  of  these  Judgments  is  taken  apart  from  Its  mem- 
bership is  such  a  class,  it  has,  no  doubt,  some  faint  meaning 
of  its  own,  but  it  loses  all  connection  and  contrast  with  the 
other  Judgments  within  the  group,  and  it  is  Just  the  extra 
fringe  of  meaning  given  by  membership  within  the  group 
which  makes  the  Judgment  significant.  "This  room  is  warm." 
Taken  as  an  isolated  fragment  of  thinking,  apart  from  the 
class  of  temperature-Judgments,  i.  c,  apart  from  any  contrast 
with  the  temperature  which  is  "cool"  and  the  temperature 
which  is  "Just  right."  such  a  Judgment  has  almost  no  signlfl- 
cance.    It  is  only  by  becoming  a  member  of  such  a  class  that 


I  Cf.  c.  p.,  Oroog,  The  Play  of  Animalt,  E.  T.  1911,  pp.  30-31.  and 
A.  B.  Taylor,  Blementa  of  lietaphyatcg,  1903,  pp.  3-S. 


•3 


EXTERNAL  ORGANISATION 


It  ceases  to  be  an  abstraction,  an  Isolated  fragment,  and  con* 
stitutes  a  vital  portion  of  our  concrete  thinking.  Thus  we 
see  that  the  external  organisation  of  "This  room  is  warm" 
in  terms  of  temperature-Judgments  is  an  integral  part  of  the 
wider  meaning  of  our  thought. 

So  too  with  the  other  departments  of  Icnowledge  within 
which  our  perceptual  Judgment  falls.  E.  g.,  the  class  of 
"practical"  Judgments  consists  of  thoughts  which  have  a 
clear  connection  with  advantageous  action,  i.  e.,  which  lead 
to  such  action.  If  our  Judgment  concerning  the  warmth  of 
the  room  is  not  a  member  of  this  class,  it  can  have  only  a 
contemplative  significance,  divorced  from  action.  It  is  only 
so  far  as  my  thought  is  externally  organised  with  reference 
to  action  that  I  rise  and  attend  to  the  furnace,  for  example, 
or  take  precautions  against  an  outbreak  of  fire;  and  the  prac- 
tical value  of  such  connection  with  such  action  speaks  for 
Itself.  The  practical  element,  then,  constitutes  an  Integral 
portion  of  the  wider  meaning  of  our  perceptual  Judgment. 

It  remains  to  ask  what  difference  membership  in  this  exter- 
nal context  makes  to  the  Judgment  itself.  Are  the  elements, 
for  instance,  out  of  which  the  Judgment  is  constructed,  in 
any  way  altered  as  our  Judgment  enters  into  some  wider  class? 
Does  the  organisation  which  we  have  called  external  remain 
merely  external,  or  does  it  penetrate  even  into  the  internal 
construction  of  the  Judgi^ent,  and  into  the  elements  out  of 
which  8  and  P  are  built  up? 

There  can  be  no  doubt  as  to  our  answer.  We  have  already 
seen  that  the  internal  organisation  is  dependent  on  the  gen- 
eral meaning  of  the  Judgment,  and  that  the  meaning  of  the 
Judgment  alters  according  as  we  regard  it  on  the  one  hand 
as  an  isolated  fragment  of  thinking,  or  on  the  other  as  a  mem- 
ber of  some  definite  class,  i.  e.,  as  externally  organised  In 
some  wider  Intellectual  context.  For  instance,  if  "This  room 
is  warm"  be  regarded  (1)  as  a  member  of  the  class  of  prac- 
tical Judgments,  and  (2)  as  not  a  member  of  such  a  class, 
there  can  be  no  doubt  that  the  connection  with  action — or 
severance  from  action,  as  the  case  may  be — enters  into  the 
selection  of  elements  out  of  which  8,  P,  and  the  whole  judg- 
ment are  built  up.  In  the  first  case,  most  of  the  temperature- 
values  selected  will  be  connected  with  well  defined  actions. 
Elements  of  "Just-rlghtness,"  for  Instance,  are  associated  with 
sitting  still;   elements  of  "coolness"  or  "warmth"  are  asso- 


IN  PERCEPTUAL  JUDGMENTS 


U 


elated  with  dlverae  operations  upon  the  thermostat  or  directly 
upon  the  furnace.  In  the  second  case,  on  the  other  hand,  every 
element  is  carefully  divorced  from  its  customary  association 
with  action,  and  is  regarded  In  a  rigidly  speculative  light.  In 
this  way  we  see  that  the  selection  of  elements  out  of  which 
the  Judgment  is  composed.  Is  governed  not  only  by  (1)  the 
meaning  of  8  and  P  and  (2)  the  meaning  of  the  Judgment  as  a 
whole,  but  also  by  (3)  the  wider  meaning  of  the  Intellectual 
context  into  which  the  Judgment  enters.  Hence  we  conclude 
that.  Just  as  8  and  P  are  externally  organised  in  the  wider 
totality  which  is  the  Judgment,  so  the  perceptual  Judgment  ii 
externally  organised  in  the  wider  totality  which  is  iU  intel- 
lectual context. 

(B)  In  Judgments  of  Experience.— Take  such  a  Judgment  as 
"The  freight-trains  crossing  the  bridge  are  becoming  yearly 
more  troublesome."  In  the  sense  in  which  we  have  under- 
stood it  previously,  this  Judgment  falls  into  at  least  the  fol- 
lowing departments  of  knowledge:— (1)  Judgments  based  on 
sense-perception.  (2)  practical  Judgments,  and— in  the  wider 
field  of  implication— (3)  social  Judgments,  (4)  physical  Judg- 
ments, etc.  Finally  it  falls  into  the  class  of  "thlnkables"  or 
Intelligent  Judgments  thought  of  as  forming  a  single  coherent 
system.  Experiential  Judgments  are  thus  externally  organ- 
ised in  much  the  same  way  as  we  have  found  to  be  the  case 
with  perceptual  Judgments. 

Let  us  proceed  to  ask  what  difference  it  makes  to  an  expe- 
riential Judgment,  to  be  externally  organised  in  this  kind  of 
way.  Hitherto  we  have  regarded  our  example  of  an  experi- 
ential Judgment  as  falling  predominantly  within  the  class  of 
sense-Judgments.  It  is  emphatically  the  noise  made  by  the 
trains  which  Is  such  a  disturbing  element,  and  the  Judgment 
as  a  whole  is  a  summing  up  of  such  noise-disturbances,  such 
offences  to  our  ear.  The  sensory  element  is  thus  very  pro- 
nounced. If,  now,  we  think  of  it  apart  from  membership  in 
such  a  class.  If  we  think  away  the  noisiness  of  the  freight- 
trains,  they  have  also  lost  their  disturbing  character— in  other 
words,  the  characteristic  meaning  of  the  Judgment  has  van- 
Ished.  Our  thought  is  thus  dependent  on  such  external  organ- 
isation for  the  significance  which  it  has  for  us,  and  member- 
3hlp  in  this  claas  is  a  legitimate  part  of  the  wider  meaning 
of  the  experiential  Judgment. 

So  too  with  the  other  classes  in  reference  to  which  our  Judg- 


v/' 


84 


EXTKRNAL  ORGANISATION 


,,x' 


A 


ment  is  extertially  organised.  Consider,  for  example,  the  prac- 
tical and  social  classes.  In  the  sense  in  which  we  have  taken 
It  hitherto,  our  Judgment  about  the  train-disturbances  Is  no 
impersonul,  contemplative  summing  up  of  evidence.  The  dis- 
turbances interfere  with  our  work,  and  to  such  an  extent  that 
we  are  impelled  to  do  soniething  about  them,  to  write  to  some- 
one, to  organise  social  pressure  and  bring  it  to  bear,  etc. 
Deprive  the  Judgment  of  its  external  organisation  In  these 
classes,  and  you  destroy  a  large  part  of  Its  signlflcance  for  us. 
Thus  we  realise  that  here  also,  the  practical  and  social  ele- 
ments constitute  a  legitimate  portion  of  the  wider  meaning 
of  our  Judgment  of  experience. 

The  same  is  the  rase  with  all  the  classes  into  which  our 
Judgments  of  experience  undoubtedly  fall,  and  our  general 
conclusion  inevitably  Is,  that  such  Judgments  are  not  «om- 
plete,  if  we  regard  them  as  units  to  be  taken  by  themselves; 
on  the  contrary,  each  Judgment  of  this  kind  enters  into  a 
wider  intellectual  context  In  which  it  obtains  most  of  the  ele- 
ments of  meaning  which  make  it  valuable  and  tigniflcant 
for  us. 

It  remains  to  ask  whether  this  external  context  is  merely 
external,  or  whether,  as  we  found  to  be  the  case  with  per- 
ceptual Judgments,  it  enters  also  Into  the  Internal  structure  of 
the  Judgment.  Do  8  and  P.  and  the  elements  out  of  which 
these  are  put  together,  remain  constant,  unaltered,  however 
their  Intellectual  context  may  vary,  or  are  some  elements  sifted 
out  and  rejected,  while  others  are  selected  and  retained,  accord- 
ing as  the  guiding-thread  of  the  external  organisation  directs? 
There  can  be  no  doubt  about  our  answer.  What  governs  the 
selection  is,  as  we  have  seen,  the  meaning  of  the  Judgment  as 
,  a  whole,  and  the  meaning  of  the  Judgment  as  a  whole  varies  in 
accordance  with  the  intellectual  context  into  which  It  enters. 
Hence  the  elements  selected  in  the  construction  of  8  and  P, 
and  of  the  Judgment  as  a  whole,  will  vary  as  the  wider  intel- 
lectual context  varies.  For  example,  If  the  wider  context 
demands  practical  and  social  action  in  order  to  put  a  stop  to 
these  noises  which  interfere  with  my  work,  then  that  aspect 
of  each  of  the  recalled  train-disturbances  becomes  selected  in 
which  the  practical  and  social  importance  of  putting  a  stop 
to  such  disturbances  is  prominent.  If,  on  the  other  hand,  the 
wider  context  assures  us  that  steps  have  been  taken  which 
will  prevent  a  repetition  of  the  disturbances,  then  each  of  the 


IN   SYMBOLIC  JUDGMENTS 


—       — '     ioS" 
85 


s/ 


recalled  irain-nolset  comes  before  us  with  the  special  label 
•over-and-donewlth."    Thus  we  se<>  that,  in  the  Judgment  of "> 
experience   also,   the    Internal    organisation    Is   through   and  > 
through  dependent  on  the  external  organisation.  S 

(C)  In  Symbolic  Judgments.— Take  such  a  Judgment  ai 
•Rome  was  occupied  by  Caesar."  m  the  sense  In  which  we 
have  understood  It  hitherto,  this  Judgment  falls  Into  at  leaet 
the  following  cla8«es:-(i)  dramatic,  even  tragic.  JudgmenU. 
(2)  historical  Judgments,  with  all  which  these,  in  turn.  Imply. 
—^.  0.,  (3)  artheologlcal  Judgments,  (4)  eplgraphical  Judg- 
ments, (5)  linguistic  Judgments,  etc.  Ultimately,  as  history 
occupies  a  certain  place  among  the  sciences.  It  belongs  to  the 
system  of  knowledge,  or  what  we  have  called  "thlnkables  " 
regarded  as  an  organic  totality.: 

What  difference  doer  such  external  organisation  make  to 
the  symbolic  Judgment?     Let  us  consider.     In  the  sense  In 
which  we  have  always  taken  it,  the  occupation  of  Rome  by 
Caesar  Is  a  dramatic  event,  an  event  of  even  tragical  signifi- 
cance.   On  the  one  side  we  have  the  Pompeians.  the  Senatorial 
party,  representing  law  and  order,  the  majesty  of  Rome     On 
the  other  side  we  have  the  "populares,"  a  mixed  set  of  ruined 
and  turbulent  citizens,  led  by  Caesar  at  the  head  of  his  Oallle 
War  veterans,  invading  their  Mother-country.     It  looks  like 
the  clash  of  Might  against  Right,  and  the  uncertainty  as  to 
which  party  and  which  leader  Is  in  the  right  adds  to  the  com- 
plex dramatic  nature  of  the  situation.     Deprive  the  Judgment 
of  the  external  organisation  in  virtue  of  which  It  becomes  a 
niember  of  this  class,  and  it  pales  into  insignificance.    Remove 
the  dramatic  element,  and  the  meaning  dwindles  away  to  a 
mere  nothing,  a  common-place  event  of  no  interest-compelling 
Importance.    In  this  way  we  realise  that  external  organisation 
in  terms  of  the  dramatic  Is  part  of  the  wider  meaning  of  our 
Judgment.    It  Is  only  when  we  euvlsage  It  as  a  great  step  in 
a  fateful  drama  that  we  appreciate  its  full  significance 

As  with  the  class  of  dramatic  Judgments,  so  also  with  the 
other  elements  in  the  external  organisation  which  constitutes 
the  intellectual  context  of  our  Judgment.  Abstract  from  this 
context  e.  g.,  the  historical  significance  of  the  judgment  cu 
off  our  Judgment  from  the  evidence  of  archeology,  from  its 
dependence  on  ancient  manuscripts,  etc.,  and  It  becomes  at 

2  A.  L.  Jones,  Logic,  pp.  260  IT. 


86 


EXTERNAL  ORGANISATION 


once  a  very  different  thing.  Events  conceived  as  unhistorical, 
e.  g.,  in  works  of  professed  flctlon,  may  have  dramatic  signifi- 
cance, but  our  attitude  towards  fictitious  events  is  sharply  dis- 
tinguished from  our  attitude  towards  events  regarded  as  his- 
torical, and  to  relegate  our  judgment  to  the  fictitious  class 
would  be  seriously  to  curtail  its  legitimate  meaning.  In  this 
way  we  realise  that  the  symbolic  judgment  cannot  be  treated 
as  a  self-sufficient  unit,  existing  by  itself  in  splendid  isolation 
from  all  other  judgments,  but  that  it  is  essentially  an  organic 
portion  of  a  wide  intellectual  context  which  endows  it  with 
the  dramatic,  historical,  and  other  elements  of  meaning  which 
make  it  valuable  and  significant  for  us.  It  is  thus  externally 
organised  in  reference  to  wider  universes  of  meaning,  and 
ultimately  in  reference  to,  and  dependence  on,  the  totality  of 
meanings,  the  system  of  thinkables,  within  which  historical 
and  dramatic  judgments  have  their  specific  places. 

As  in  the  case  of  perceptual  and  experiential  judgments,  we 
must  now  ask  whether  this  external  organisation  remains 
merely  external.     Does  it  merely  affect  the  judgment  as  a 
whole,  or  does  It  enter  into  the  internal  organisation  also,  and 
modify  the  details  of  the  judgment?    As  we  have  seen,  8,  P, 
and  the  judgment  as  a  whole  are  built  up  out  of  elementary 
experiences;    our  question  thus  means.  Are  these  elements 
independent  of  the  external  organisation,  do  they  remain  con- 
stant, however  the  external  context  may  vary— or  does  the 
external  context  modify  them  down  to  their  minutest  details? 
Let  us  consider.    The  elements  used  in  constructing  our  judg- 
ment are  such  stuff  as  dreams  are  made  of,  as  well  as  sober 
history:— experiences  of  sunny  skies,  of  crowds,  of  panic  and 
triumph,  and  so  forth,  called  up  by  association  with  the  words 
"Rome,"  "was,"  "occupied,"  "by,"  "Caesar."    Of  these  possible 
associates,  as  we  have  already  seen,  only  such  are  selected  as 
are  compatible  with  the  meaning  of  the  judgment  as  a  whole. 
That  is  to  say,  the  associates  called  up  by  each  word  are  pro- 
foundly modified  by  their  connection  with  the  associates  of 
the  other  words  which  together  go  to  build  up  the  complex 
internal  structure  of  the  judgment.    Are  these  elements  fur- 
ther modified  by  the  entrance  of  the  judgment  into  a  wider 
class?    Does  it  make  any  difference  to  the  associates  selected, 
if  the  judgment  Is  regarded  as  fictitious  or  as  historical,  as 
dramatic  or  as  commonplace?    There  can  be  no  doubt  as  to 
our  answer.    If  the  judgment  is  dramatic  and  tragic  we  cei- 


IN   SYMBOLIC   JUDGMENTS 


87 


talnl:  tend  to  select  such  elements  of  our  crowd-experiences, 
of  our  panic  and  triumph-experiences,  etc.,  as  are  connected 
for  us  with  the  dramatic  and  tragic.  If,  on  the  other  hand, 
the  judgment  is  regarded  as  commonplace,  we  select  mainly 
such  elements  of  our  crowd-experiences,  etc.,  as  are  connected 
with  every-day  feelings.  Thus  we  see  that  the  external  con- 
text into  which  the  judgment  enters,  profoundly  modifies  the 
details  of  internal  organisation,  and  in  fact,  that  the  construc- 
tion which  gives  us  the  symbolic  judgment  varies  as  the  exter- 
nal organisation  varies,  or,  as  we  have  seen  in  the  previous 
judgment-types,  the  internal  organisation  is  through  and 
through  dependent  on  the  wider  intellectual  context.3 

(D)  in  Transcendent  Jidgments.— Consider  such  a  Judg- 
ment as  "God  is  a  substance  with  infinite  attributes."  In  the 
sense  in  which  we  have  understood  it  hitherto,  i.  e.,  taken 
ideally,  as  realising  all  which  it  attempts  to  accomplish,  such 
a  judgment  can  not  be  said  to  fall  into  any  larger,  wider,  more 
inclusive  class.  It  is  formed  by  taking  various  attributes,  such 
as  extension  and  thought,  and  expanding  these  to  infinity,  and 
as  the  resulting  concept  of  God  Is  exyllcitly  all-inclusive — 
including  not  only  all  humanly  possible  experience,  but  also 
all  possible  experience  in  general,  human,  aagellc,  and  Divine 
— It  embraces  already,  in  its  internal  context,  every  universe 
of  meaning.  There  thus  remains  nothing  outslae,  in  refer- 
ence to  which  it  could  be  said  to  be  "externally"  organised.  In 
other  words,  transcendent  judgments,  taken  ideally,  are  co- 
extensive with  the  ultimate  class,  the  class  of  thinkables. 

It  should,  however,  be  clear  from  the  nature  of  the  case, 
that  a  judgment  which  really  and  in  actual  fact  was  all-in- 
clusive, and  embraced  in  the  unity  of  a  single  act  of  thought 
not  only  all  humanly  possible  experience,  but  also  an  infinity 
of  experiences  of  which  human  beings  cannot  even  frame  a 
clear  positive  concept — i.  e.,  a  judgment  which  really  tran- 
scends human  experience — cannot  be  made  by  a  human  being. 
In  other  words,  it  is  only  ideally  that  a  transcendent  judg- 
ment can  be  said  to  have  no  external  context.    In  actual  prac- 

3  Of.  W.  B.  rill»bury.  Fundamentals  of  Psychology,  1917,  p.  340 : 
"The  outlines  of  black  and  white  that  constitute  the  words  start  the 
association  processes  which  lead  to  the  Ideas,  and  these  associates  are 
controlled  by  the  wider  setting  and  wider  knowled^je  of  the  Inaly^dual 
at  the   moment.      .  .    The  revival  of  the  pari  lor  exp<»npnces  la 

controlled  by  the  laws  of  association  and  by  the  contewt  In  a  degree 
that  practically  amounts  in  many  coses  to  new  construction."  ( lUIlcg 
mine.) 


88 


EXTERNAL  ORGANISATION 


tice,  tbe  attempts  to  think  metaphysically  tend  to  be  one- 
sided, largely  formal,  finite,  and  imperfect.  They  are,  in  fact, 
symbolic  extensions  of  experience,  labeled  with  the  formal 
demand  that  they  should  be  extended  to  infinity.  But  this 
demand  remains  purely  formal,  and  expresses  an  ideal  which 
we  cannot  realise  in  actual  concrete  thinking.  In  the  case 
before  us,  for  example,  we  think  of  God  as  possessing  attrib- 
utes which  come  within  the  realm  of  human  experience. 
When  we  attempt  to  magnify  each  of  these  attributes  beyond 
the  scope  of  possible  human  experience,  i.  e.,  to  infinity,  we 
tend  to  lose  ourselves.  For  in  infinity,  in  that  which  is  pre- 
sumed to  lie  beyond  human  experience,  the  distinctions  which 
have  meaning  and  value  within  our  experience  cease  to  apply. 
Infinite  space,  for  example,  cannot  be  measured  out  in  Inches 
or  centimetres;  infinite  time  is  hopelessly  incommensurable 
with  our  minutes  and  hours;  and  the  infinite  spirituality  of 
the  Divine  cannot  be  expressed  in  terms  of  finite  propositions 
taken  from  empirical  psychology.  The  symbolic  ideal  of  a 
better  Self,  that  is,  a  Self  better  than  our  actual  Self,  but  dis- 
tinctly conceived  as  within  the  range  of  human  possibility, 
has  meaning  and  value  for  the  direction  of  our  lives.  But  the 
transcendent  concept  of  an  absolutely  perfect  Self,  a  Self  which 
transcends  infinitely  the  possibility  of  human  realisation,  is  so 
remote  that  we  cannot  ev:n  form  a  clear  positive  conception 
of  what  it  means;  and  its  value  for  our  lives  diminishes  in 
direct  proportion  to  its  remoteness.^ 

In  dealing,  then,  with  actual  judgments  of  this  group,  we 
may  treat  them  as  a  slightly  more  extensive  kind  of  symbolic 
Judgment;  in  which  case,  all  that  we  have  found  true  of  the 
symbolic  judgment  will  hold  good  here  also.  If  these  judg- 
ments are  one-sided  and  imperfect,  then  it  is  possible  for 
them  to  have  an  external  context:  and  if  they  have  an  exter- 
nal context,  then  the  general  meaning  of  the  judgment  will 
alter  according  to  the  external  context  into  which  it  enters. 
For  example,  if  we  think  of  God  chiefly  as  a  merciful  judge 
of  the  weaknesses  of  humanity — i.  e.,  in  reference  to  the  class 
"merciful  judges" — our  thought  acquires  shades  of  meaning 
which  differentiate  it  sharply  from  the  thought  of  God  in  some 
other  context,  e.  g.,  as  the  object  of  mystical  enjoyment,  that 
experience  of  infinite  unity  in  which  we  are  alone  with  the 


«  Cf.  H.  Sldjfwlok.  Methods  of  Ethic»,  pp.  18-22. 


"  ^  I  ^ 

IN  TRANSCENDENT  JUDGMENTS  89 


Alone.B  In  the  same  way.  so  far  aa  we  regard  Judgments  of 
this  group  as  essentially  and  in  fact  extended  symbolic  Judg- 
ments, the  external  organisation  will  enter  into  the  internal 
structure  of  the  Judgment,  and  will  govern  the  selection  of  the 
elements  out  of  which  S,  P,  and  the  Judgment  as  a  whole  are 
built  up.  In  other  words,  transcendent  Judgments,  as  actually 
Judged  by  human  beings,  are  dependent,  as  to  their  internal 
organisation,  down  to  the  -minutest  details,  upon  the  wider 
class  within  which  they  fall,  and  this  class  is  ultimately  the 
class  of  thinkables,  the  ideally  complete  organisation  of  all 
which  can  consistently  be  thought. 

Conclusion — The  Ultimate  Intellectual  Standard. — ^If  we 
now  put  together  what  we  have  discovered  about  the  meaning 
of  external  organisation  for  the  various  types  of  Judgment, 
certain  conclusions  stand  out  with  especial  prominence. 
First  and  foremost,  no  Judgment  whatever  stands  by  itaelf, 
but  -each— iFTBn  integral  portion  Of  sOme  wider 'universe  of 
meaning,  wlilch  constitutes  Its  intellectual  context.  Per- 
ceplual  Judgments  are  portions  of  a  concrete  texture  of  thought 
which  is  by  no  means  confined  to  the  perceptual  level.  This 
intellectual  context  embraces,  as  we  have  seen,  not  only  per- 
ceptualTseBsoixlndgmEnfs,  but  also  summings  up  of  these  In 
classified  form — i.  e.,  is  continuous  with  experiential  and  sym- 
bolic Judgments.  Ultimately,  as  extending  into  the  field  of 
"thinkables,"  it  is  continuous  with  the  intellectual  context  of 
transcendent  Judgments.  Judgments  of  experience  are  simi- 
larly portions  of  a  wider  context  which  on  the  one  side  forms 
part  of  our  popular,  perceptual  thought,  and  on  the  other  is 
intellectually  continuous  with  those  summings  up  of  experi- 
ence out  of  which  science  is  bom.  Ultimately,  as  being  con- 
tinuous with  the  texture  of  science,  this  intellectual  context 
is  continuous  with  the  symbolic  extension  of  experience  which 
reaches  out  after  infinity  and  is  called  transcendent.  So  too 
the  intellectual  context  of  symbolic  Judgments  is  on  the  one 
side  experiential,  and,  on  the  other,  transcendent,  while  tran- 
scendent Judgments  seem  partly  to  be  symbolic,  partly  to 
belong  to  an  all-inclusive  universe  of  meaning.  Every  Judg-' 
ment,  then,  is  part  of  a  wide  system  of  meaning,  which  extends 
with  unbroken  intellectual  continuity  in  the  direction  of  what 
we  have  called  transcendent  thinking. 

BCf.  PlotinuB,  Enneiidt,  Bk.   VI,  chapter  Iz,  sec.   10  (In  Bakewelk, 
Source  Book  in  Ancient  PMlotophy,  p.  393). 


/ 


90 


EXTERNAL  ORGANISATION 


Let  us  ask  further,  are  the  systems  of  meaning  to  which 
different  judgments  belong,  themselves  different?    For  exam- 
ple, does  "The  room  is  warm"  belong  to  a  different  universe 
of  meaning,  a  wholly  different  Intellectual  context,  from  that 
Into  which  such  Judgments  enter  as  "Rome  was  occupied  by 
Caesar,"  or  "God  Is  a  substance  with  infinite  attributes?"    Our 
answer  must  be,  No.    They  belong,  of  course,  to  distinguish- 
able systems  of  meaning,  as  sense-judgments  can  be  distin- 
guished from  historical  judgments,  or  as  a  judgment  based 
on  the  warmth  which  we  perceive  with  our  senses  can  be  dis- 
tinguished from  a  judgment  about  God.  whom  we  do  not  per- 
ceive with  our  senses.    But  these  systems  are  only  relatively 
distinguishable— they   are   not   absolutely   severed   from   one 
another.    Ultimately  all  form  parts  of  one  and  the  same  great 
system.    In  the  case  of  the  special  sciences,  for  Instance,  we 
saw  that  a  thread  of  mathematical  and  logical  thinking  runs 
through  and  so  far  connects  and  unifies  most  of  our  concrete 
thinking,     if  we  apply  this  to  the  present  case,  we  can  see 
that  all  systems  of  meaning,  however  diverse  In  appearance, 
are  at  one  at  least  In  this,  viz.,  that  they  are  all  alike  systems 
of  meaning,  that  logical  thought  and  Intelligible  significance 
enters  Into  them  all— in  a  word,  that  they  one  and  all  belong 
to  the  widest  and  ultimate  totality  of  "Intelllglbles"  or  "think- 
ables."    In  this  way  we  come  to  realise  that  the  ultimate  sys- 
tem, the  circle  of  widest  meaning  to  which  our  judgments  can 
possibly   belong,   whether   they   are   perceptual,   experiential, 
symbolic,  or  transcendent,  is  the  totality  of  thinkables.  and 
that  in  an  ideally  complete  intellectual  organisation  of  our 
sensory  consciousness,  the  various  elements  which  go  to  form 
the  8  and  P  of  our  judgments— "the  room,"  "frelght-traln-dls- 
turbances,"  "Rome."  and  "God."— and  Indeed  every  judgment 
of  whatever  type,  must  be  rational,  comprehensible,  and  think- 
able through  and  through,  so  as  to  be  fit  without  further  trans- 
formation, to  take  their  place  In  a  completely  Intellectuallsed 
experience,  in  which  all  elements  whatever  would  be  clearly 
interrelated,  and  be  organic  through  and  through  with  mean- 
Ing.e 

Our  final  conclusion,  then,  concerning  the  intellectual  ele- 
ment in  judgment  is  this:— The  standards  of  identity  and 


8Cf.   Plato's  Ideal  of  Dialectic,  as  develoned  In  Renuhitr,    Rk    vt 
ad  fln..  and  F.  H.  Bradley,  Principles  0/  Loifc.ppI  449^61.    '  "*•   ^^' 


ULTIMATE  INTELLECTUAL  STANDARD 


91 


diversity  or  difference  are  subordinate  concepts  within  the 
wider  conception  of  organisation,  and  the  standard  of  internal 
organisation  is  subordinate  to  the  conception  of  external  organ- 
isation. The  unity  of  whatever  can  be  consistently  thought  as 
belonging  to  a  single  intellectual  system  is,  then,  the  ultimate 
standard  of  the  Intellectual  side  of  Judgment.  It  remains  to 
inquire  into  its  validity.? 

iThl»  ultimate  standard  ia  vrhat  Kant  calls  the  Up  '^  of  Self- 
consciousness — i.  e.,  of  a  single  ultimate  experience.  Kaui  .  ^metimes 
calls  it  the  "transcendental  unity  of  apperception."  Of.  <"  ligue  ot 
Pure  Reason,  tr.  BlelJcelJoHn,  pp.  82-86.  Cf.  also  Bosanq  et.  Logic. 
Vol.  I,  p.  144 :  "The  course  of  Judgment  within  the  present  whole 
of  perception  is  determined  by  connections  which  refer  beyond  that 
accidental  whole,  to  other  more  comprehensive  totalities,  and  nlti- 
mately,  in  every  case,  to  the  system  of  the  known  world.  The  connec- 
tions thus  prescribed  between  part  and  part  within  some  systematic 
whole  are  necessary  connections." 

FOR  FURTHER  RBADINQ 

B.  Bosanquet,  Logic,  Vol.  I,  pp.  72-92.  W.  B.  Plllsbury,  The 
Fundamentals  of  Paychology,  pp.  335-344.  Chr.  S<lgwart,  Logic,  Vol. 
II,  pp.  508-528. 


EXBRCISBS 

1.  What  is  the  wider  intellectual  context  of  the  following  Judg- 
ments, and  how  far  does  it  enter  into  their  internal  organisation : 
llje  Ice  looks  slippery.     These  skates  feel  sharp.     This  key  is  rusty? 

2.  What  is  the  wider  intellectual  context  of  the  following  Judg- 
ments, and  how  far  does  It  enter  into  their  Internal  organlaations : 
In  the  spring  a  young  man's  fancy  lightly  turns  to  thoughts  of  love. 
Beans  and  cucumbers  nearly  always  die  of  some  blight.  Life  Ic  qot 
what  It  used  to  be? 

3.  1\'3iat  Is  the  wider  Intellectual  context  of  ithe  following  Judg- 
ments, and  how  far  does  It  enter  lnt6  their  internal  organisation: 
Water  is  H20.  Marlus  conquered  the  Cimbri  and  Teutones.  Some 
day  the  air-plane  will  supersede  the  aatomoblle? 

4.  What  is  tfhe  wider  Intellectual  context  of  the  following  Judg- 
ments, and  how  far  does  it  enter  into  their  internal  organisation: 
Things  In  themselves  are  unknowable.  I  have  taken  aU  knowledge  to 
be  my  province — I  shall  be  omniscient  The  Future  Life  will  be  the 
present  life  over  again,  but  raised  to  tlie  nth  power? 


CHAPTER    IX 


THE  INTELLECTUAL  ELEMENT  AND  VALIDITY. 

The  Question  of  Validity.— So  far  we  have  seen  that  the 
function  of  Intellect  In  judging  Is  to  split  up  the  material 
of  sensory  consciousness,  to  take  it  apart  Into  its  elements, 
and  then  re-shape  it  nearer  to  the  desire  for  relevance,  con- 
sistency, systematic  unity.  This  is  done  by  introducing  the 
standards  of  ideutity-ln-difference,  dlfTerence-in-identity,  and 
organisation,  both  internal  and  external,  until  at  last  the 
material  of  the  sensory  consciousness  has  been  so  worked 
over  that  it  is  able  to  take  its  place  in  a  single  organised 
system,  in  which  every  element  is  rational,  relevant,  coherent 
with  every  other  element,  and  the  whole  structure  down  to 
its  minutest  details  is  consistent,  thinkable  through  and 
through,  and  organic  with  a  meaning  which  constitutes  one 
great  Identity-indifference,  a  single  system,  an  ideal  indi- 
vidual. 

All  this,  however,  is  merely  descriptive.  It  tells  us  how 
the  intellect  functions,  what  it  does.  But  there  is  a  further 
question,  the  question  of  validity.  Granted  that  the  intellect 
functions  in  this  kind  of  way,  is  what  it  does  leffitimatef 
Can  we  justify  the  great  changes  brought  about  by  intel- 
lectual organisation?  By  what  right  do  we  analyse  and 
reconbtruct?  That  our  meddling  intellect  mis-shapes  the 
beauteous  forms  of  things,  mutilates  reality  and  imprisons 
it  within  a  net-work  of  man-made  frames,  conceptual  abstrac- 
tions in  which  is  neither  life  nor  truth— in  this  view  poet 
and  philosopher  are  frequently  at  one,  and  never  mort,  so 
than  at  the  present  day.  That  the  work  of  "discursive" 
thought  is  thus  infected  with  falsity,  is  a  conclusion  not 
lightly  to  be  set  aside.  The  question  must  therefore  be  faced 
— How  far  is  the  work  of  intellect  valid? 

Here,  for  the  sake  of  clearness,  we  must  introduce  a 
distinction  between  a  more  general,  and  a  more  special  ques- 
tion. What  our  poets  and  philosophers  mean,  when  they 
suspect  the  intellect  of  misleading  us,  is  that  truth  resides 

92 


THE  QUESTION  OF  VALIDITY 


93 


in  intuition,  sensation,  sympathy,  immediate  awareness, 
whereas  intellect  gives  us  an  awareness  which  is  mediate, 
not  the  thing  itself,  but  a  conceptual  model,  a  structure  which 
we  can  substitute  for  the  reality.  We  can  understand  this, 
because  we  have  ourselves  constructed  it.  It  works  as  well 
as  if  it  were  the  original,  but— it  is  not  the  original.  This 
objection  to  the  work  of  intellect  opens  up  a  more  general 
question  than  we  are  at  present  in  a  position  to  discuss.  It 
compares  and  balances  the  respective  value-claims  of  intellect 
and  intuition,  or  intellect  and  sensation,  and  thus  presupposes 
an  answer  to  two  more  special  questions,  (1)  concerning  the 
validity  of  intuition  or  sensation,  and  (2)  concerning  the 
validity  of  intellect.  So  far,  we  have  only  answered  the 
first  of  these  more  special  questions.  We  have  treated  of 
the  sensory  element,  in  abstraction  from  the  intellef*tual 
element.  It  remains,  therefore,  to  attack  the  second  of  these 
special  questions.  We  must  leave  on  one  side  the  question 
of  sensation  and  sensory  validity,  and  examine  how  far.  If 
at  all,  the  Intellect,  qua  intellect,  is  valid,  i.  e.,  the  question 
of  intellectual  validity.  After  this  question  is  answered.  If 
we  succeed  in  discovering  the  work  of  intellect  to  be  Intel- 
lectually valid,  we  can  then  proceed  to  the  general  question, 
and  ask  how  far  the  working  of  a  mind  which  is  intellectually 
aans  peur  et  sans  reproche  compares  with  sensory  validity, 
as  a  factor  in  attaining  reliable  knowledge  of  reality. 

Let  us  take  an  example.  If  the  truth  of  a  scientific  hypoth- 
esis is  called  in  question,  we  can,  as  we  say,  verify  It  by 
an  appeal  to  sensory  experience.  This  is  true,  and  has  been 
already  considered.  But  there  is  a  prior  question,  viz.,  how 
far  the  hypothesis  is  Intellectually  satisfactory,  how  far  the 
intellectual  structure,  the  conceptual  model,  is  really  Intel- 
ligible, whether  it  really  hangs  together  and  Is  rational  and 
meaningful.  It  is  the  conditions  of  this  meaningfulness  which 
we  must  now  examine.  Let  us  take  a  concrete  instance  from 
the  field  of  simultaneous  equations.  "If  three  hens  lay  on 
the  average  as  many  eggs  as  four  ducks,  and  the  number 
of  eggs  laid  in  a  month  by  six  hens  and  six  ducks  Is  a  hundred 
and  eighty,  what  is  the  weekly  average  of  each  hen  and  each 
duck?"  The  intellectual  element  In  the  solution  consists 
in  the  introduction  of  sharply  differentiated  identities  snch 
as  X  and  y,  in  such  a  form  that  the  conditions  of  the  problem 


94       INTELLECTUAL  ELEMENT  AND  VALIDITY 


ii' 


are  expressed  somewhat  thus:  "3x=4y,  and  6x+6y=180X7." 

~30 
The  further  manipulations  of  these  conventionalised  Identi- 
ties according  to  the  rules  of  algebra  or  geometry  Inform  us 
with  mathematical  certainty,  that  the  weekly  average  of  each 
hen  is  four  eggs,  and  of  each  duck  three  eggs.  Here,  then, 
are  judgments  which  are  Intellectually  valid.  On  what  does 
their  intellectual  validity  depend? 

It  depends  (1>  on  the  introduction  of  identlty-in-difference. 
If  X  did  not  have  a  core  of  identity  in  the  various  propositions. 
In  spite  of  its  varying  fringe  of  relations.  If,  for  Instance,  It 
meant  in  the  second  equation  jomethlng  entirely  different 
from  what  it  meant  In  the  first,  no  result  could  be  reached. 
It  depends  (2)  on  the  Introduction  of  dlfference-in-Identlty ; 
for  If  X  and  y  did  not  have  some  variations,  some  differences 
of  meaning  in  their  varying  contexts,  then,  as  we  have  seen, 
no  movement  of  thought  could  take  place;  nothing  would  be 
judged.  It  depends  (3)  on  the  organisation  of  these  identi- 
ties and  differences  with  reference  to  one  another  in  a  single 
act  of  thought;  for  instance,  if  the  first  and  second  equations 
were  not  somewhere  brought  together,  no  conclusion  could 
be  reached.  Finally  it  depends  (4)  on  the  external  organi- 
sation of  these  conventionalised  elements  within  the  wider 
system  of  algebra  or  geometry,  with  all  which  this  implies. 
The  result  Is  reached  by  adhering  strictly  to  the  rules  of 
algebra  or  geometry,  i.  e.,  to  the  rules  of  mathematics,  which 
Is  a  kind  of  applied  logic  and  belongs  to  the  system  of  what- 
ever can  be  thought.  If  we  sum  up  what  we  have  seen,  we 
can  state  that  intellectual  validity  in  the  case  before  us 
consists  in  observing  strictly  the  rules  upon  which  organi- 
sation of  intellectualised  elements  within  a  single  consistent 
system  depends.  So  far  as  the  analysis  and  subsequent  recon- 
struction are  governed  strictly  by  reference  to  the  ideal  of 
this  single  system,  the  result  is  intellectually  satisfactory. 
So  far,  however,  as  any  of  these  rules  are  not  observed — e.  g.. 
If  the  elements  are  not  Identities,  or  are  not  to  some  extent 
different,  or  are  not  organised  Internally  or  externally — so 
far  no  result  can  be  reached  with  which  we  can  be  Intellectu- 
ally satisfied. 

Let  us  now  proceed  to  ask  how  far,  in  our  various  typical 


IN  JUDGMENTS  OF  PERCEPTION 


98 


forms  of  Judgment,  the  Intellectual  structure  admits  of  Intel- 
lectual validity. 

in  Judgments  of  Perception. — Take  such  a  Judgment  as 
"This  room  is  warm."  As  we  have  already  seen,  sensation 
alone  assures  us  primarily  of  a  feeling  of  warmth.  The  Judg- 
ment, however,  that  the  roo,n  is  warm,  adds  something 
further,  an  element  of  interpretation,  which  we  have  regarded 
as  intellectual.  This  element  consists,  as  we  have  seen,  of 
an  analysis  of  the  sensory  consciousness  into  certain  ele- 
mentary experiences  which  are  then  reconstructed,  not  merely 
in  reference  to  present  sensation,  but  also  in  the  light  of  a 
wider  system  of  knowledge,  partly  experiental  and  partly 
symbolic,  partly  practical  and  partly  reaching  out  into  physics 
and  logic  with  all  which  these  imply — i.  e.,  ultimately  the 
elementary  experiences  are  reconstructed  in  terms  of  the 
single  system  of  organised  knowledge,  of  what  can  consist- 
ently be  thought.  It  is  this  reference  to  the  wider  structure 
which  enables  us  to  pass  beyond  the  present  sensation  and 
state,  not  merely  that  we  feel  warm,  but  that  the  room  is 
warm,  and  the  furnace  probably  requires  attention,  or  there 
may  be  danger  of  a  fire,  etc.  The  <n»oiia/'*nai  aii^m""*,  thfip. 
consists^  in^  realising,  in  making  concrete,  the  tines  of  intel- 
lectual continuity  which  give  our  perceptual  judgment  Its 
place  in  the  system  of  thinkables. 

On  what  does  the  validity  of  this  procedure — if  It  ia  valid — 
depend?  Let  us  consider  the  steps  we  have  taken,  in  order. 
The  first  step  consists,  as  we  have  seen,  of  analysing  our 
sensory  experience  into  elements  which  are  conventionalised, 
taken  out  of  their  sensory  contexts  and  made  discontinuous, 
cut  off  and  fixed  by  the  mind  so  as  to  retain  a  certain  identity 
of  meaning,  however  various  the  intellectual  contexts  into 
wliich  they  may  subsequently  be  thrown.  These  mental 
counters,  then,  which  are  thus  utilised  as  bricks  In  building 
up  the  intellectual  structure,  are  what  we  have  called  "identi- 
ties-in-ditference."  Those  used  in  constructing  the  logical 
subject  of  discourse — the  room — are  predominantly  spatial 
experiences,  and  those  from  which  we  construct  the  logical 
predicate — warm — are  predominantly  temperature-values.  If 
these  elements  were  not  conventionalised,  if  one  identical 
meaning  did  not  underlie  them  and  keep  them  substantially 
the  same  in  different  contexts,  if  they  remained  vague  and 
fluctuating   in   meaning, — then   farewell   to   consistency   and 


96        INTELLFXTUAL  ELEMENT  AND  VALIDITY 


unity,  i.  «'..  to  intellectual  validity.  For  what  is  inconsistent 
is  invalid,  and  what  does  not  form  a  unity  is  a  multiplicity 
without  coherence  or  consistency.  As  far,  then,  as  these 
elementary  experiences  are  strictly  rtxed  by  the  mind  and 
used  as  "identltles-in-difference,"  i.  «•..  as  retaining  the  self- 
same core  of  meaning,  whatever  the  Intellectual  context  into 
which  they  may  enter,— so  far  we  have  a  basis  upon  which  a 
consistent  and  intellectually  valid  thought-structure  may  be 
erected.  Conformity  to  the  standard  of  identity-in-ditference. 
then,  is  a  condition  sivr  qua  non  of  intellectual  validity 

A  second  step  in  the  intellectual  procedure  is  the  Introduc- 
tion of  the  standard  of  dlfference-in-identity,  i.  e.,  of  different 
fringes  of  meaning  according  as  our  "identities"  enter  dif- 
ferent contexts.  We  have  already  seen  that  apart  from  such 
difference,  no  movement  of  thought,  and  thus  no  judgment, 
could  take  place.  The  Introduction  of  difference-in-identity— 
a  fringe  of  difference  which  does  not  annul  the  underlying 
Identity— is  thus  a  second  necessary  condition  sine  qua  non 
of  intellectual  validity. 

The  third  step  is  organisation,  internal  and  external.  I£ 
the  elementary  experiences  are  not  brought  together  and 
unified,  i.  e.,  organised  so  as  to  give  us  the  complex  structures 
8  and  P.  then  there  is  no  subject  of  discourse  and  no  logical 
predicate,  which  means  that  nothing  is  judged  about  anything, 
t.  e.,  no  judgment  takes  place.  Further,  it  8  and  P  are  not 
brought  together,  if  "the  room"  and  "warm"  are  not  held 
together  in  a  sin-rle  act  of  thought  which  unifies  them  without 
annulling  their  differences,  no  judgment  takes  place.  For 
judging  is  essentially  a  function  of  unity,  and  we  certainly 
unify  the  S  and  P  concepts  in  judging  that  8  Is  P,  tL^  room  i« 
warm.  In  other  words,  internal  organisation  is  a  conditio 
sine  qua  non.  a  necessary  condition  of  judgment.  Further, 
If  the  lines  of  organisation  which  have  thus  given  us  the 
internal  structure  of  the  judgment  are  not  intellectually  con- 
tinuous with  a  wider  intellectual  structure— If  the  judgment 
is  not  continuous  In  meaning  with  temperature-judgments, 
practical  judgments,  and  ultimately  with  the  whole  organi- 
sation of  rational  experience — then  It  is  inconsistent  and 
irrational,  j.  e'.,  inlelleclually  unsatisfactory.  Thus  we  see 
that  it  is  only  so  far  as  our  perceptual  judgment  Is  intellectu- 
ally continuous  with  the  system  of  thlnkables—  i.  e.,  only  so 


IN  JUDGMENTS  OF  EXPERIENCE 


97 


far  as  it  la  relevant,  consistent,  and  rational  through  and 
through,  that  it  can  be  regarded  as  intellectually  satlsfactorjr. 

In  Judgments  of  Experience. — Take  such  a  Judgment  as 
"The  freight-trains  crossing  the  bridge  are  growing  more 
troublesome  every  year."  As  we  have  seen,  the  process  by 
which  the  senory  consciousness  is  here  raised  to  the  intel- 
lectual level,  consists  in  splitting  up  the  spatial  and  temporal 
continuum  and  selecting  elementary  experiences  of  train- 
disturbances,  taking  them  from  their  sensory  context  and 
transforming  them  into  mental  counters,  identlties-in-differ- 
ence  which  are  then  utilised  in  the  further  construction  which 
builds  up  S  and  P  and  gives  us  the  organisation  which  is  our 
Judgment— a  structure  not  merely  Internally  organised,  but 
in  its  main  lines  intellectually  continuous  with  the  wider 
structure  of  practical  Judgments,  and  ultimately  of  all  which 
can  rationally  and  consistently  be  thought  in  a  single  system 
of  meauing.  Our  question  is,  on  what  does  the  validity  of 
this  Intellectualising  process — if  it  i*  valid— depend?  For 
instance,  take  the  first  step.  Would  the  procedure  be  intel- 
lectually satisfactory  if  our  analysis  did  not  result  in  giving 
us  conventionalised  elements,  Identities-in-difference?  Let 
us  see.  If  there  is  no  identical  reference-point  governing  the 
selection  of  elements  out  of  which  8  and  P  are  to  be  con- 
structed, then  the  fif-concept  will  be  composed  of  all  kinds  of 
heterogeneous  elements  without  real  unity — a  mixture  of 
vague,  fluctuating  experiences  not  all  strictly  relevant  to  the 
concept  "train  disturbances."  Such  unintelligent  groupings 
would  certainly  not  be  clear  enough  or  sufficiently  to  the 
point  to  be  used  as  an  intellectual  subject  of  discourse,  and, 
in  fact,  as  we  have  seen  in  perceptual  Judgments,  the  strict 
introduction  of  identity-in-difference  would  seem  to  be  a  aine 
qua  non  of  intellectually  valid  thinking.  What  is  true  of  the 
elementary  experiences  which  are  grouped  together  in  order 
to  form  £1  and  P  is,  of  course,  true  also  of  £1  and  P  themselves 
and  indeed  of  the  general  meaning  of  the  Judgment.  Each  of 
these  mu')t  have  its  own  clearly  apprehended  meaning,  an 
Identical  direction  of  thought  underlying  any  change  of  intel- 
lectual context,  if  the  resultant  structure  is  to  be  intellectually 
satisfactory. 

In  the  second  place,  the  introduction  of  difference-in-identity, 
as  we  have  already  seen,  is  similarly  a  aine  qua  non  of  valid 
thinking,  indeed  of  thinking  at  all.    Without  some  difference 


y« 


INTF.Ll.KCTUAL  KLKMKNT  AND  VALIDITY 


reBulting  from  th        .ylng  fringe  of  relations  contributed  by 
the  contexts  Into  wh    h  S  and  P.  for  Instance,  enter,  no  move- 
ment of  thouKht  cou'  1  take  place,  nothing  would  be  Judged. 
In  the   third   place,  organisation   of  the  varloua  elemenUry 
traln-dlsturbanoe  experiouceB  bo  as  to  form  S  and  P,  and  of 
S  and  P  thtmselves  within  the  single  act  of  thought  which 
Is  the  Judgmpnt.  Is  necessary;  and  finally,  if  the  general  lines 
of  Internal  orsanlsatlon  are  not  strictly  continuous  with  the 
general  lines  on  which  the  whole  system  of  thinkable,  con- 
sistent, and  rational  Judgments  is  constructed,  then  the  result 
falls  to  cohere,  and  is  thus  Intellectually  unsatisfactory.     In 
this  way  we  realise  that  Intellectual  validity  in  the  case  of 
experiential  Judgments  depends  on  strict  conformity  to  the 
Intellectual  standards  of  Identity,  difference,  and  organlsaUon. 
It  Is  only  so  far  as  the  analysis  results  in  idenUties  with 
fringes  of  difference,  organised  so  as  to  form  an  Integral  por- 
tion of  the  vast  system  which  Includes  all  which  can  be  con- 
sistently and  rationally  thought,  that  the  Judgment  of  experi- 
ence can  be  regarded  as  intellectually  satisfactory. 

In  Symbolic  Judgments.— Symbolic  Judgments  have  already 
been  dealt  with,  at  least  in  principle,  in  the  slmultaneoua 
equation  case   considered  above.     What  makes  this  a  case 
of  the  "symbolic"  type  of  Judgment  Is  not  so  much  the  fact 
that  algebraic  rymbols  were  employed  in  its  solution,  as  that 
it  reconstructs  for  us,  by  indirect  methods,  a  summing  up 
of  experiences   which   goes   beyond   what   we   have  actually 
experienced.     The  statement  of  the  average  number  of  eggs 
to  be  expected  per  hen,  for  instance.  Is  more  than  a  mere 
summing  up  of  past  experiences;   it  gives  us  a  rule  which 
holds  e.  g.,  for  future  experiences,  for  experiences  which  have 
not  been,  and  Indeed  may  never  be  ours,  in  a  word,  the  Judg- 
ment moves  In  the  field  of  possible  human  experience.      It 
thus  belongs  to  the  sphere  of  what  we  have  called  "symbolic" 
Judgments,  and  we  may  take  what  we  saw  there  and  apply 
it  briefiy  to  our  typical  Instance  of  a  symbolic  Judgment, 
"Rome  was  occupied  by  Caesar."     The  steps  by  which.  In 
this  typical  case,  the  sensory  consciousness  becomes  raised 
to  the  .Intellectual  level  consist   (1)   in  the  analysis  which 
results  In  mental  counters  composed  of  blue-aky  experiences, 
panic  and  triumph  experience,  etc.,  taken  out  of  their  original 
sensory  contexts  and  fixed  by  the  mind  in  the  form  of  identl- 
ties-ln-difference,   (2)   in  the  introduction  of  difference,  *.  e., 


IN  TRANSCKNDKNT  JUDGMENTS  » 

different  ■hade*  of  meaning  accordlog  to  variation!  of  Intel- 
Jectual  context— into  ttie  "Identitlee"— and  (S)  the  organi* 
■ation,  both  internal  and  external  of  theie  differentiated  Iden- 
tities, which  results  in  giving  us  a  judgment  which  does  not 
Btand  by  itself,  but  is  part  and  parcel  of  whatever  ii  rational 
and  meaningful,  and  helps  to  constitute  the  tingle  system  of 
whatever  can  consistently  be  thouRht.  It  is  unnecessary  to 
Inquire  in  detail  concerning  the  intellectual  validity  of  this 
Judgment.  Briefly  and  In  principle,  it  Is  only  so  far  as  these 
Intellectual  standards  of  identity,  difference,  and  organisa- 
tion are  followed,  only  so  far  as  the  resulting  structure  really 
does  constitute  an  integral  portion  of  the  system  of  thlnk- 
ables,  only  so  far  as  it  is  intellectually  continuous  with  all 
which  is  rational,  consistent,  and  coherent,  that  it  can  be 
regarded  as  intellectually  satisfactory. 

In  Transcendent  Judgment*.— Transcendent  Judgments  are, 
as  we  have  seen,  a  kind  of  extended  symbolic  Judgment,  so 
that  the  conclusions  as  to  intellectual  validity  which  we  have 
found  to  hold  good  in  the  case  of  symbolic  Judgments  can  be 
transferred,  without  alteration  in  principle,  to  transcendent 
Judgments  also.  And  in  fact.  If  we  examine  the  thought  of 
our  professed  metaphysicians,  we  find  without  much  difficulty 
that  It  is  on  the  standards  already  studied  that  they  rely  for 
the  intellectual  validity  of  their  constructions.  The  attempt 
to  construct  the  outlines  of  the  Absolute  Experience  is  almost 
always  guided  by  considerations  of  systematic  consistency,  and 
the  ideal  of  rational  thinkablllty  Is  openly  acknowledged  as  the 
highest  standard  to  which  one  can  appeal.  We  shall  there- 
fore conclude  without  further  examination,  that  in  such  Judg- 
ments as  "God  is  a  substance  with  Inflnite  attributes,"  "Things- 
in-themselvea  are  unknowable."  "The  real  is  the  rational."  and 
Bo  forth,  the  Intellectual  validity  of  such  constructions  depends 
upon  strict  conformity  to  the  standards  of  identity,  difference, 
and  organisation,  and  that  It  is  only  so  far  as  such  Judgments 
are  strictly  consistent  and  cohere  in  a  single,  all-inclusive  uni- 
verse of  rational  meaning,  that  they  are  regarded  as  Intel- 
lectually satisfactory.! 

Conclusion— Intellectual  Validity.— If  we  now  put  together 
what  we  have  discovered  in  our  discussion  Hitherto,  we  realise, 
that  while  all  Judgments  have  a  sensory,  as  well  as  an  Intel- 

.  *  ^'•.,''-  P-^T-   'I-    nradley.   Appearance  and  Reality,  latest  edition 
Appendix  I ;  nosanquet.  Logic  Vol.  I,  pp.  3-8.  *  eaition, 


100      INTELLIXTUAL  ELEMP:NT  AND  VALIDITY 

lectual  aspect,  it  is  only  so  far  as  tliey  conform  to  intellectual 
standards  that  they  can  claim  intellectual  validity.  It  is  only 
so  far  as  intellectually  irrelevant  elements — such  as  we  find 
vaguely  embodied  in  the  continuous  stream  of  sensory  con- 
sciousness— are  removed,  and  we  have  strict  organisation  of 
strictly  inteliectualised  identities  within  a  single  system  which 
includes  In  principle  all  that  can  consistently  be  thought — 
that  the  resulting  structure  can  be  regarded  as  intellectually 
satisfactory.  A  judgment,  then,  is  intellectually  valid,  precisely 
In  so  far  as  it  is  fitted,  without  further  qualification  or  trans- 
formation of  meaning,  to  enter  into  a  system  of  relations  which 
includes  every  thought  which  is  rationally  consistent,  and  thus 
itself  intellectually  satisfactory,  the  kingdom  oi  Truth.2 

2  Cf.  Kant.  Critiiiur  of  I'urv  liinmn  (tr.  Melklejohn),  pp.  26-27. 
Thp  vIp.v-  tnken  In  the  tt'xt  Is  approximately  the  paiae  as  Kant's  when 
he  says  that  only  that  wlilch  reason  constructs  atxiordlng  to  rational 
principles  Is  entirely  Intelligible  and  satisfactory. 


FOR  FURTHER  READING 

P.  II.   Bradley,  Pt  iiiriphs  of  Logic.  IJk.  I,  chapter  i. 
Logik,  (2nd  Kdlt.),  pp.   194-197,  409-426. 


B.  Erdmann, 


EXERCISES 

1.  On  what  does  the  Intellectual  validity  of  the  following  judg- 
ments depend  :  You  are  looking  sun-burned.  This  leaf  Is  turning  red. 
This  new  varnish  feels  sticky? 

2.  On  whRt  dopii  the  Intellectual  validity  of  t<he  following  judg- 
ments depend  :  We  usually  put  on  the  storm  windows  towards  the 
end  of  Oi'tober.  Our  tomai /es  Hpen  well  Indoors,  if  we  allow  the 
sun  to  get  to  them.     The  neighbor's  baby  nearly  always  cries  at  night? 

3.  On  what  does  the  intellectual  validity  of  the  following  judg- 
ments depend :  None  but  the  brave  deserve  the  fair.  Demoathenes 
was  a  great  orator,  but  a  poor  statesman.     .5340  —  2189  =  31.51  ? 

4.  On  what  does  the  intellectual  validity  of  the  following  judg- 
ments depend  :  Ail  genuine  knowledge  is  independent  of  experience. 
We  shall  be  as  Go<l.  knowing  ixith  good  and  evil.  As  It  was  in  the 
beginning.  Is  now,  and  ever  sliall  he,  world  without  end. 


CHAPTER  X 


THE  VALIDITY  OP  JULGMENT 

The  Problem.— So  fur  we  have  discovered  by  analysis  of  our 
thought  two  aspects  oi  '^very  juegment.  (1)  the  sensory,  and 
(2)  the  Intellectual.    We  have  further  seen  that  each  of  these 
aspects  has  its  own  lawS;  and  that  it  is  only  by  strictly  con- 
forming to  these  laws  that  each  aspect  possesses  validity 
within  its  own  sphere.    So  far  as  our  thought  is  sensory,  it 
is  valid  provided  that  it  is  a  continuous  sensory  expansion  from 
the  focus  of  sensory  consciousness,— continuous,  that  is  to  say, 
in  space  and  time.    So  far  as  it  is  intellectual,  our  thought  is 
valid   so  far  as  it  constitutes  an  integral  portion   of  that 
organised  totality  which  ideally  contains  all  which  can  con- 
sistently be  thought  and  can  rationally  cohere  in  a  single 
system  of  meaning.     Sensory  continuity  is  one  thing;  Intel- 
lectual consistency  Is  another;  and  we  have  already  seen  that 
these  are  not  perfectly  proportioned  to  one  another  in  our 
concrete  thinking.    In  perceptual  judgments,  the  sensory  ele- 
ment Is  almost  everything;  but  as  we  advance  towards  sym- 
bolic and  transcendent  judgments  we  notice  more  and  more 
the  gulf  between  what  sensation  can  give  and  what  the  ideal- 
ising Intellect  demands.    The  sensory  element  can  be  spread 
out.  so  to  speak,  so  as  to  cover  the  field,  not  merely  of  actual, 
but  also  of  possible  human  experience.    But  as  we  gradually 
approach  the  place  where  the  symbolic  begins  to  pass  Into  the 
transcendent  type  of  thinking,  the  sensory  covering  has  become 
so  thin  that  at  last  it  is  totally  Inauequate  to  satisfy  the  needs 
of  intellect.    Sense  and  intellect  are  thus,  to  some  extent  at 
least,  heterogeneous,  and  sense  covers  a  less  wide  field  than 
Intellect.   What  is  their  inter-relation,  and  which  of  them  plays 
the  major  part  In  contributing,  not  to  the  specifically  sensory, 
or  specifically  intellectual  validity  of  judgment,  but  to  the  gen- 
eral validity  of  our  thinking?    This  is  our  present  problem. 

Ideallem.— Bntfiy  thinkers,  from  Pla*o  down,  have  assigned 
the  palm  to  iLTJellect.  For  such  thinkers,  "the  sensory,"  or 
the  content  of  the  sensory  consciousness,  is  not  an  object  of 

101 


102 


THE  VALIDITY  OF  JUDGMENT 


W\ 


■1;    ' 
-  i 


Bt'ict  knowledge.     It  is  too  vague  and  fluid,  and  refuses  to 
lend  Itself  to  the  manipulations  of  accurate  and  systematic 
thought.    It  is  only  so  far  as  we  conform  strictly  to  intellectual 
standards,  and  leave  behind  us  the  sensory  element,  that  we 
attain  to  truth,  or  knowledge  of  real  Being,  a  knowledge  which 
extends  infinitely  beyond  what  oui  limited  senses  can  hope  to 
realise.    For  Descartes  and  Leibniz,  for  instance,  in  modern 
philosophy,  sense  is  simply  confused  thinking,  thinking  con- 
fused by  connection  with  our  bodily  sense-organs,  and  it  is 
only  so  far  as  the  mind  separates  itself  from  these  disturbing 
influences  and  thinks  by  Itself,  that  it  can  attain  to  clear  and 
distinct  apprehension  of  its  object.    So  too  in  our  own  day  it 
is  not  difficult  for  a  writer  like  Bradley  to  show  that  the  chief 
viewpoints  of  empirical  science  fail  to  conform  strictly  to 
intellectual  standards,  and  thus  present  us  with  a  kind  of 
knowledge  which  deals  only  with  phenomena,  not  with  Reality 
— i.  e.,  not  with  the  kind  of  object  which  would  fulflU  the  ulti- 
mate aspirations  of  pure  Intellect.    The  great  Idealists  have 
thus  almost  all  disparaged  sensation  and  exalted  intellect,  to 
such  an  extent  that,  as  notably  in  the  systems  of  Plato  and 
Hegel,  intellect  tends  to  occupy  the  entire  field,  and  the  field 
of  knowledge  is  taken  to  coincide  with  the  field  of  transcendent 
thought. 

Sensualism.— A  differgnt  group  of  thinkers,  of  whom  per- 
haps Condillac  is  the  chief  representative,  regard  the  sensory 
element  as  of  predominant  importance.  For  such  thinkers,  to 
judge  is  to  perceive  a  relation  between  two  ideas.  The  per- 
ception of  such  a  relation  is  a  matter  of  comparison,  and  com- 
parison is  a  matter  of  attending  to  two  sensations.  Judg- 
ment thus  means  attending  to  two  sensations.  But  attention 
itself  is  not  an  intellectual  act.  Attention  means,  having  our 
capacity  for  feeling  wholly  taken  up  by  the  impressions  made 
upon  our  sense-organs,  and  these  Impressions  are  modifica- 
tions of  our  conscious  selves,  i.  e.,  of  our  sensibility.  Thus  we 
see  that  judgment  is  a  matter  of  having  our  capacity  for  feel- 
ing wholly  taken  up  by  two  impressions,  or.  more  simply,  hav- 
ing our  sensibility  modified  in  two  ways,  ».  e.,  having  two  sen- 
sations. Attention  is  thus  not  a  specifically  "intellectual" 
operation.  It  is  simply  a  question  of  being  r->nscious  of  sen- 
sations, and  such  thinkers  tend  to  regard  al.  .he  more  elabo- 
rate structures  of  science  and  philosophy  as  valid  only  so  far 


SOLUTION  OF  THE  PROBLEM 


103 


a'  they  can  be  reduced,  without  remainder,  to  simple  sensa- 
tlons.i 

Solution  of  the  Problem. — Both  these  views  are  one-sided. 
It  cannot  be  too  strongly  insisted  upon,  that  sensation  with- 
out intellectual  organisation  is  blind,  and  intellect  without 
sensory  content  is  empty.  Everything  which  we  regard  as 
meaningful,  rational,  clear-cut,  and  intelligible  is  to  some 
extent  the  result  of  intellectual  operation.  A  "pure"  sensa- 
tion, t.  e.,  a  sensation  purified  of  every  intellectual  element, 
would  be  without  organisation,  without  identity  or  fixity,  a 
fleeting  psychical  entity  which  we  could  never  quite  grasp  and 
apprehend.  In  fact,  seizing,  grasping,  and  fixing  is  essentially 
the  work  of  intellect,  an  intellectual  operation  necessary  to 
understand  anything,  introducing,  as  it  does,  order,  system, 
rationality,  meaning  into  what  would  otherwise  be  incoherent 
and  chaotic.  It  piclcs  out  from  the  sensory  consciousness 
everything  which  is  relevant,  and  lets  the  rest  go.  It  tele- 
scopes the  sensation,  so  to  speak,  and  ma  ,  \s  the  meaningful 
elements  stand  out  in  sharp  relief.  In  other  words,  the  intel- 
lectual concept  is  the  sensation,  but  only  so  far  as  the  sensa- 
tion contained  elements  of  meaning.  It  is  the  essence,  the 
meaning,  the  concentrated  extract,  as  it  were,  of  the  sensory 
consciousness.  Jnst  as  a  bottle  of  beef-extract  is  supposed  to  | 
represent  the  concentrated  food- value  of  the  ox,  so  does  the  | 
intellectual  concept  renresent  the  concentrated  meaning-value 
of  the  sensory  consciousness.  Scientific  method  is  simply  an 
efficient  intellectual  machine,  into  which  one  puts  the  vague 
and  confused  mass  of  feelings,  sensations,  etc.,  in  order  to  grind 
out  clear-cut  elements  which  can  be  used  for  constructing 
science. 

On  the  Ocher  hand,  without  sensory  content  intellect  can 
accomplish  nothing.  One  cannot  make  bricks  without  straw; 
and  the  application  of  scientific  methoc  cannot,  however 
methodic  the  scientist  may  be,  extract  from  the  data  more 
than  is  there  to  be  extracted.  No  amount  of  scientific  manip- 
ulation of  mathematical  or  physical  material,  for  instance,  can 
produce  valuable  decisions  on  ethical  or  religious  questions. 


1  Btienne  Honnot  de  CondlUae,  Traiti  iles  Sensations,  I'arls  and 
T»ndon,  1754.  See  Rand,  Modern  Classical  Philosophers,  pp.  347-375. 
This  way  of  thinking  Is  usually  attributed  to  the  British  school  of 
thought  "which  commences  with  lyjcke.  ("f.  l/ucke's  Essay  (1G90- 
1700),  Bk.  tl.  Cf.  also  J.  S.  Mill,  Examination  of  Sir  William  Hamil- 
ton'»  Philosophy,  chapter  xl  (lUnd,  pp.  690-702). 


104 


THE  VALIDITY  OF  JUDGMENT 


just  as  no  amount  of  card-indexing  our  ethical  or  religious 
convictions  can  tell  us  anything  about  the  validity  of  biological 
theories  of  evolution.  We  need,  it  Is  true,  all  the  applied 
logic,  all  the  scientific  method,  of  which  we  are  capable.  But 
we  must  recognise,  and  never  allow  ourselves  to  forget,  that 
logical  acumen  alone  will  never  lead  to  valuable  results.  It  is 
necessary  also  to  have  material  with  which  to  work,  and  this 
material  comes  from  the  sensory  consciousness.  Both  Intel- 
lect and  sensation  are  necessary,  if  we  are  to  attain  to  results 
of  general  validity. 

Let  us  take  an  example.  Any  one  who  has  had  to  solve 
many  problems  by  means  of  simultaneous  equations,  for 
instance,  knows  well  how  easy  it  Is  to  make  some  slight  error 
in  the  preliminary  analysis  which  results  In  the  two  a?  and  y 
equations.  The  conventionalised  expression  often  fails  to  rep- 
resent strictly  the  concentrated  extract  of  the  popular  expres- 
sions of  general  language.  In  such  cases,  the  subsequent  oper- 
ations with  X  and  y  may  take  place  with  consummate  skill, 
but  if  anything  vital  has  been  omitted  or  added,  the  final 
result,  however  valid  intellectually,  fails  of  attaining  general 
validity.  The  answer,  as  we  say,  is  wrong,  though  some  mark 
may  be  given  for  the  working.  There  has  been  a  mistake  In 
fact,  and  it  is  only  by  patient  reference  to  the  material,  by 
repeated  sense-experiences,  that  we  can  hope  to  rectify  such 
mistakes.2 

Application.— Let  us  apply  this  solution  briefly  to  our  typi- 
cal instances.  (1)  The  validity  of  "The  room  is  warm"  will 
depend  wholly  upon  whether  this  judgment  is  a  correct  inter- 
pretation of  the  sensory  consciousness,  the  feeling  of  warmth 
which  I  undoubtedly  xperience.  My  judgment  consists  in  an 
organisation  of  this  consciousness,  the  rpplicatlon  of  scientific 
method  with  all  its  standards,  in  order  to  extract  from  it  the 
essence  or  meaning-value  which  it  contains.  The  validity  of 
the  result  depends,  in  the  first  place,  upon  whether  the  analysis 
and  reconstruction  is  itself  intellectually  valid,  t.  e.,  whether 
it  is  consistent  and  rational—this  Is  a  sine  qua  Twn— but  also. 
In  the  second  place,  whether  the  result  harmonises  with  the 
sensory  starting-point.  If  I  conclude  that  the  temperature  of 
the  room  is  normal,  while  my  sensations  continue  to  assure 
me  that  I  feel  warm,  then  something  is  wrong.    The  hypothe- 


2Cf.  Erdmann,  Lnglk,  pp.  372-413,  esp.  p.  374. 


APPLICATION  OF  SOLUTION 


105 


sis  of  the  room's  being  warm  must  be  succeeded  by  a  question 
as  to  whether  I  myself  am  In  some  pathological,  feverish  state, 
etc.  That  is  to  say,  as  in  the  simultaneous  equation  above, 
there  may  have  been  some  mistake  about  the  preliminary 
analysis,  the  pathological  symptoms  having  been  overlooked. 
In  other  words,  in  order  to  verify  a  perceptual  Judgment  it  is 
necessary  (1)  to  be  sure  that  the  result  is  intellectually  satis- 
factory, and  (2)  to  be  certain  that  it  really  does  represent  the 
meaning,  the  concentrated  essence,  of  the  sensory  conscious- 
ness which  it  professes  to  interpret,  and  this  can  only  be 
assured  by  patient  reference  to  the  sensory,  as  well  as  to  the 
intellectual  side  of  the  experience. 

(2)  So  too  in  the  experiential  example.  In  such  a  judg- 
ment as  "The  freight-trains  crossing  the  bridge  are  growing 
more  troublesome  in  recent  years,"  error,  or  lack  of  validity, 
is  almost  always  a  matter  of  lack  of  thoroughness  in  the  intel- 
lectual analysis.  The  disturbance  is  annoying,  and  without 
really  making  a  clear-cut,  exact,  scientific  comparison  with 
previous  experiences,  we  "How  ourselves  to  jump — ^without 
thinking — to  the  conclusiou  that  it  is  more  troublesome  than 
it  used  to  be.  Or  it  may  be  merely  that  we  are  personally 
growing  more  sensitive.  It  will  be  important,  in  dealing  later 
with  the  railway  company,  to  know  precisely  which  of  these 
is  the  case.  The  verification  of  our  conclusion,  therefore,  will 
involve  both  the  application  of  strict  scientific  method  and 
patient  reference  to  the  sensory  consciousness  which  extends 
back  from  the  present  to  the  past  cases  of  similar  disturb- 
ances. The  Judgment  of  experience  will  thus  be  valid  so  far 
as  it  is  a  correct  interpretation  of  the  experiences  in  ques- 
tion, i.  €.,  (1)  correctly  put  together  in  accordance  with  intel- 
lectual standards,  and  (2)  correctly  applied  to  the  particular 
experiences  of  disturbing  freight-trains. 

(3)  The  case  of  symbolic  Judgments  has  already  been  con- 
sidered in  principle  in  dealing  with  the  simultaneous  equation 
example  above.  It  remains  to  apply  our  results  briefly  to  the 
judgment  of  Rome  being  occupied  by  Caesar.  The  validity  of 
our  conclusion  depends  on  the  correctness  with  which  we  have 
interpreted  the  printed  text  of  our  history  book,  which  in  turn 
goes  back  to  the  interpretation  of  various  classical  manuscripts 
and  archeologlcal  evidences.  It  is  well  known  that  momen- 
tous conclusions  in  history  have  at  times  been  based  upon  very 
slender  evidence.    The  ideal  of  reaching  valid  concIusionB  in 


'-'-^ 


1()6 


VALIDITY  OF  JUDGMENT 


!h  ^?     'u     °'  •*®°^^»'»«  °ot  only  the  strictest  use  of  clear 
thinking,  but  also  the  most  careful  study  of  the  data  before 
the  student-i.  c.  the  visual  sensations,  or  sensory  conscious- 
ness  of  the  reader.    Only  thus  can  we  be  sure  that  the  Inter- 
pretative structure  Is  really  based  upon  experiential,  sensory 
foundations.    Both  Intellectual  and  sensory  validity  are  nec- 
essary to  secure  the  general  validity  of  the  symbolic  Judgment 
(4)  Transcendent  judgments,  in  the  nature  of  the  case  are 
incapable  of  direct  sensory  verification.    All  that  we  can  do  is 
(1)  to  test  our  thinking  concerning  "things-in-themselves."  or 
whatever  our  transcendent  entities  may  be.  by  referencTe  to 
intellectual  standards,  and  then  (2)  to  connect  it  with  what- 
ever sensory  experience  we  may  have  which  bears  upon  the 
question.    These  ultimate  conclusions  of  speculative  thought 
these  metaphysical  edifices,  are  all  supposed  to  represent  the 
final  truth  of  our  experience,  to  give  the  concentrated  essence 
or  meaning-value  of  experience  as  a  whole.    But  this  includes 
our  actual  experiences  here  and  now.  so  that  the  Intellectual 
acumen  of  the  philosopher  represents  only  one  side  of  the 
question      His  results  must   really  apply  somewhere  to  our 
empirical  experiences  also,  if  they  are  to  be  regarded  as  of 
general  validity.     Not  only  intellectual,  but  sensory  validity 
also  is.  then,  necessary  in  the  case  of  transcendent  judgments 
Conclusion-Theory  of  Judgment.-Let  us  now  try  to  put 
together  the  whole  of  our  preceding  discussions,  let  us  prac- 
tise what  we  have  just  been  preaching,  and  endeavor  to  extract 
the  kernel  of  meaning  from   the  material   which   has  sur- 
rounded it  in  varying  ways  from  the  first  page  to  the  present 
Qqr  (IgTHllllBlnn  lfi>.that  ludgmpnt  la  thp.Jclellectual  organisa- 
Uan-af,8eusQry  ^perience.   the   introducti^T^f   intPilPPH.ni 
standards  into  the  sensory  consciouanp^r^^c-T^rcl^:^^  in 
Pjgceofjhejven^t  vague  seng-y  flow.  TTliiPI^^irL^tel- 
l^^^Haligedjggensej^icysJu^!^^ 
idgaLpf, organisation,  the  system  of  jnowaUles.    ThiT^c.^m 
is  not  only  thinkable  through  and  thFHUibTbut  must  be  con- 
nected with  the  sensory  consciousness  in  such  a  way  that  our 
judgments  can  be  verified,  can  be.  not  merely  thought    but 
known.    The  conceptual,  intellectuallsed  essence  must  be  the 
essence  of  the  sensory  experience,  i.  e.,  must  give  us  a  mean 
ing  which  is  not  a  pure  creation  of  intellectual  manipulation 
but  is  implicitly  present  from  the  very  first,  embedded  in  our 
experience  even  at  the  sensory  level.    Judgment,  then,  is  both 


THEORY  OF  JUDGMENT 


107 


jenaory  and  Intellectual;  it  is  the  Intellectual  organisation  of 
sensory  experience,  and  Is  valid  precisely  so  far  as  it  is  what 
it  professes  to  be.  If  the  sensory  side  of  the  experience  is 
acceptable  to  direct  sensory  apprehension,  and  the  intellectual 
organisation  is  thoroughly  conslitent,  and  if,  finally,  the  Judg- 
menTIirthe  Intellectual  organisation  o/  the  jensory  experience 
in  question,  then  the  Judgment  is  valid. 

FOR  FURTHER  READINQ 

B.  Bosonquet,   Ijoglc,  Vol.  I,  pp.   72-92.     F.  H.  Bradley.   Principle* 
of  Logic,  Bk.   I,  chapter  1.     H.  Lotze,  Logic,  pp.  140-148. 


EXERCISES 

1.  On  what  does  the  validity  of  the  following  Judgments  depend: 
These  gloTea  are  very  comfortable.  This  water  ia  too  hot  to  drink. 
This  grain  elevator  ia  larger  than  that? 

2.  On  what  does  the  validity  of  the  following  Judgments  depend: 
We  nearly  always  go  to  church  on  Sunday.  As  a  general  rule,  the 
children  seem — so  far  as  I  ihave  seen — to  prefer  the  slide  to  the 
swings.     We  Si.'em  to  walte  up  to  life  again  when  the  spring  comes? 

3.  On  what  doe«  the  validity  of  the  following  Judgments  depend: 
Conscience  is  but  a  word  which  cowards  use,  devised  at  first  to  keep 
the  strong  in  awe.  Shakespeare  borrowed  nearly  all  his  plot*  from 
other  writers.     Blue  litmus  paper  turns  red,  when  dipped  into  acid? 

4.  On  what  does  the  validity  of  the  following  Judgments  dep«id: 
The  terminatloo  of  thLs  life  is  the  beginning  of  a  new  existence.  The 
aim  of  my  life  is  mystical  absorption  in  Divinity.  The  vision  of 
absolute  beauty  raises  us  above  the  human  level? 


APPENDIX  TO  PART  I 


NEGATION 


The  Problem.— Traditional  logic,  from  the  time  of  Arle 
totle  to  the  present  day,  has  recognised  a  distinction  of  judg- 
ments ad  affirmative  and  negative.  "8  Is  P"  is  an  affirmative 
judgment,  and  "S  Is  not  P"  is  a  negative  judgment.  For  tra- 
ditional logic  this  distinction  Is  of  major  Importance.  Modern 
logic,  on  the  other  hand,  regards  the  distinction  as  of  minor 
Importance.  Lotze  treats  judgment  as  the  answer  to  a  ques- 
tion "Is  8  r  Pt"  (i.  e.,  Does  S  stand  In  a  certain  relation  to 
P?),  and  observes  that  whether  we  answer  Yes  or  No  makes 
no  difference  to  r,  t.  e.,  to  the  logical  character  of  the  relation. 
Whether  affirmed  or  denied,  It  remains  the  relation  8  r  P,  and 
a  distinction  where  there  is  no  difference  of  relation  is  of 
little  Importance  for  logic.  Wundt  and  Erdmann  sompwhat 
similarly  regard  the  distinction  as  of  secondary  importance, 
and  we  have  accordingly  not  dealt  with  It  in  the  text.  But 
unless  properly  understood,  negation  gives  rise  to  so  many 
difficulties  of  interpretation,  that  it  is  necessary  to  deal  with 
them  in  an  appendix.  The  two  chief  difficulties  are,  (1)  that 
negation  is  subjective,  and  (2)  that  negation  is  indefinite. 

Is  Negation  Subjective? — Let  us  take  a  few  Instances. 
Things-in-themselves  are  not  knowable.  Virtue  is  not  square 
or  hexagonal.  No  men-who-are-not-brave  deserve  the  fair.  47 
plus  89  do  not  make  130.  All  is  not  gold  that  glistens.  Stone 
walls  do  not  a  prison  make,  no.*  iron  bars  a  cage.  There  is 
no  such  thing  as  "apperception."  I  am  not  in  love.  This  color 
Is  not  brown.  .  .  .  These  examples  cover  the  whole  field 
of  judgment,  and  with  such  instance?  in  view  we  can  ask,  Does 
negation  give  us  any  information  which  could  be  called  posi- 
tive? Does  it  add  to  our  knowledge  of  reality?  Has  it,  in  a 
word,  objective  value,  or  Is  It  merely  subjective? 

Let  us  consider.  "Things-in-themselves  are  not  knowable." 
Does  this  tell  us  anything  about  "the  knowable,"  or  about 
"things-in-themselves?"  Does  it  even  assert  indubitably  that 
there  are  such  entities  as  thlngs-in-themselves  or  knowledge? 

iOB 


NEGATION 


109 


For  modern  logic,  on  the  whole,  the  answer  to  each  of  these 
queations  Is  No.  "Virtue  is  not  square"  seems  to  note  a  posi- 
tive failure  on  our  part  to  connect  ethical  and  mathematical 
values,  perhaps  comparable  to  the  failure  to  get  to  know  any- 
thing about  thlngs-in-themselves.  To  Itnow  that  "no  cowards 
deserve  the  fair"  does  not  tell  us  that  any  one  doea  deserve 
the  fair.  Perhaps  merit  does  not  enter  Into  the  case  at  all. 
To  know  that  "47  plus  89  do  not  make  130"  does  not  tell  us 
what  they  do  make.  Prom  such  considerations,  a  tendency  has 
arisen  to  regard  negation  as  registering  a  failure  of  some  Ideal 
experiment  of  ours.  We  have  constructed,  in  the  unsubstantial 
region  of  the  imagination,  a  relation  8  r  P  and  proceed  to 
interrogate  reality,  to  see  whether  it  will  accept  our  hypothe- 
sis. If  we  can  verify  it,  If  reality  accepts  our  ideal  sugges- 
tion, well  and  good;  we  have  added  to  the  sum  of  knowledge. 
But  if  reality  refuses  to  accept  our  hypothesis,  we  must  try 
again.  The  only  positive  conclusion  Is  that  we  have  failed. 
We  cannot  even  be  certain  that  reality  Is  otherwise  than  we 
have  supposed.  It  may  be  merely  that  we  have  failed  to  con- 
nect our  supposal  properly.  Many  a  correct  hypothesis  In 
science  has  been  abandoned  for  a  time  because  in  the  then 
state  of  knowledge  It  could  not  be  verified.  In  such  cases  It  Is 
not  possible  to  say  of  srch  a  relation  8  r  P  either  that  It  ia, 
or  that  It  ia  not.  All  that  can  be  stated  correctly  Is  that 
we  do  not  know  whether  or  no.  We  do  not  know  whether 
thlngs-in-thembelves  are  absolutely  unknowable,  whether  ethics 
and  mathematics  are  hopelessly  disparate  departments  of  expe- 
rience, whether  the  fair  can  or  can  not  be  deserved  by  any 
combination  of  manly  qualities.  All  that  we  do  know  Is  that 
we  have  failed  hitherto  to  discover  a  satisfactory  answer.  In 
other  words,  the  value  of  negation  is  subjective  rather  than 
objective.  It  throws  us  back  upon  ourselves,  and  ends  In  the 
Socratlc  recognition  of  Ignorance. 

Is  this  all  that  we  can  say?  Is  the  search  after  knowledge, 
as  the  psychologists  tell  us,  a  matter  of  trial  and  error,  hit 
or  miss?  Are  we  to  say  the  whole  value  of  the  negative  judg- 
ment consists  In  registering  a  miss,  in  realising  that  we  are 
somehow  in  error  and  must  try  again?  Even  If  so,  we  can- 
not stop  with  this  statement.  For  to  know  that  we  are  In 
error  Is  to  know  something  positive,  to  add  to  some  extent  to 
the  sum  of  human  knowledge.  It  may  not  tell  us  much  about 
eplstemology  or  ethics  or  mathematics,  but  It  does  tell  us 


■ 


110 


APPENDIX 


■omething  about  ourBelves.  But  since  we  are  also  elements 
within  the  real  world,  the  Socratic  conviction  of  our  own 
Ignorance  will  have  »ome  objective  signiiicance.  To  know  that 
we  have  failed,  that  we  cannot,  at  least  at  present,  verify  our 
hypothesis,  involves  some  positive  knowledge  about  the  uni- 
verse of  discourse  within  which  our  Ideal  experiment  Is 
applied.  Reallty-as-we-conceive-it  rejects  our  hypothesis. 
Good.  We  must,  then,  have  some  conception  about  reality,  and 
our  failure  amounts  to  this,  that  we  recognise  an  incompati- 
bility between  two  of  our  conceptions  about  reality.  One  is 
accepted  as — at  least  in  part — verified.  The  other  is  rejected, 
at  least  as  being  inconsistent  with  the  first.  It  Is  possible  that 
the  first  is  not  entirely  inconsistent  with  the  second;  it  may 
be  merely  that  we  cannot,  are  not  in  a  position  to  realise  the 
deeper  viewpoint  which  will  ultimately  reveal  an  underlying 
unity  and  consistency.  We  thus  recognise  an  inconslitency 
within  the  realm  of  knowledge,  and  it  is  this  recognition  of 
Inconsistency  which  convinces  us  of  failure  and  throws  us 
back  jpon  ourselves.  The  negative  Judgment  is  thus  at  least 
the  positive  recognition  of  inconsistency,  otherness  or  differ- 
ence in  the  world  of  knowledge.  We  can,  if  we  wish,  define 
this  as  "subjective."  But  if  we  can  recognise  differences 
within  one  sphere  of  knowledge,  why  not  also  in  another, 
(say)  in  physics  or  mathematics? 

Let  us  consider  further.  So  far  we  have  been  proceeding 
upon  a  somewhat  one-sided  view.  ^Ve  have  been  assuming 
that  the  suggested  relation  r  is  aflHrmative  in  character.  Let 
us  now  take  the  other  alternative.  Let  us  suppose  the  rela- 
tion to  be  negative,  a  suggestion  that  perhaps  8  and  P  are 
objectively  different.  We  form  the  ideal  hypothesis  that  a 
square  is  not  a  circle,  that  virtue  is  not  three-cornered,  that 
cowardice,  at  any  rate,  does  not  me;  It  feminine  favor.  We 
proceed  to  interrogate  reality,  and  find  that  it  accepts  our 
idea.  Well  and  good.  The  hypothesis  is  verified,  and  the  sum 
of  objective  knowledge  is  increased.  We  have  established  a 
fact,  the  fact  of  some  objective  difference,  and  can  no  longer 
maintain  our  Socratic  pose  of  ignorance.  We  know,  and  we 
know  by  means  of  a  negative  Judgment.  The  negative  Judg- 
ment can  thus  serve  to  give  us  objective  knowledge. 

It  is  thus  misleading  to  regard  the  affirmative  Judgment  as 
monopolising  objective  knowledge,  and  to  treat  the  negative 
Judgmeut  as  exclusively  subjective.     The  truth  seems  rather 


NEGATION 


HI 


to  be  tbat  both  forms  alike  possess  not  only  a  subjective,  but 
also  an  objective  reference.  If  then  in  affirmation  we  are  in 
undeniable  contact  with  reality,  the  same  statement  holds 
good  of  negation  also.  In  both  cases  we  are  apprehending  an 
objective  relation,  a  relation  which  really  obtains  between  ele- 
ments of  reality.  The  difference  between  affirmation  and  nega- 
tion ia  not  the  difference  between  establiahing  and  failing  to 
establish  contact  with  reality.  Contact  is  established  in  both 
cases.  The  difference  is  only  in  the  kind  of  relation  appre- 
hended. There  are,  on  the  one  hand,  relations  of  inclusion  or 
identity,  and  on  the  other,  relations  of  exclusion  or  differ- 
ence; and  both  kinds  of  relation  are  equally  objective.  "An 
electric  bulb  is  not  a  typewriter."  This  deals  with  a  perfectly 
objective  relation.  An  electric  light  is  other  than,  different 
from,  a  typewriter.  You  cannot  substitute  the  one  for  the 
other.  Recognition  of  such  differences  and  distinctions  in  the 
objective  world  is  often  even  more  essential  to  our  safety  than 
recognition  of  identities.  "That  ladder  is  not  safe,"  "The  Ice 
is  not  strong  enough,"  "The  paint  is  not  dry,"  "The  train  does 
not  stop  here,  unless  you  ask  the  conductor,"  "X  is  not  to  be 
trusted  in  money  matters."  If  we  were  unable  to  rise  above 
the  subjective  stage  of  asking  questions  and  failing  to  answer 
them,  if  we  failed  to  establish  contact  with  reality  in  such 
practical,  every-day  negations,  who  can  doubt  that  our  life,  as 
Hobbes  puts  it,  would  be  "nasty,  brutish,  short"? 

Negation,  then,  has  an  objective  reference.  How  are  we  to 
classify  the  "subjective  failure"  which  is  sometimes  a  fact  of 
experience?  Can  we  classify  it  as  either  affirmative  or  nega- 
tive, or  does  It,  perhaps,  fall  outside  this  distinction?  Let  us 
consider.  In  every  Judgment,  whether  affirmative  or  negative, 
so  long  as  we  succeed  in  establishing  contact  with  reality,  so 
far  as  reality  accepts  our  ideal  suggestion,  we  have  a  sub- 
jective reaction — the  reaction  which  we  may  roughly  designate 
as  satisfaction  in  our  success.  Failure,  then,  is  something 
different.  It  is  not  our  reaction  either  when  we  establish  an 
affirmative  relation,  or  when  we  establish  a  negative  relation. 
It  arises  only  when  we  do  not  succeed  in  attaching  our  float- 
ing idea  to  reality,  when  this  remains  a  floating  idea  and  we 
still  do  not  know  whether  reality  accepts  it  or  no.  We  have 
asked  our  question  and  cannot  answer  it.  Our  attitude  is  one 
of  painful  suspense,  with  a  certain  sense  of  failure.  Our  sug- 
gestion obstinately  refuses  to  leave  the  unsubstantial  region 


112 


APPENDIX 


of  the  imagination.  Put  almply,  we  do  not  succeed  in  making 
our  Judgment.  We  do  not  Judge.  The  uense  in  which  Sigwart 
and  others  take  negation  must  be  interpreted,  then,  as  lnvolr> 
ing,  not  negative  Judgment,  but  absence  of  Judgment.  That  is 
a  subjective  failure,  and  results  in  the  Socratic  confession  of 
ignorance.  But  we  must  not  confuse  it  with  the  establish- 
ment of  a  negative  relation  between  8  and  P  in  the  objective 
world.  Either  we  Judge,  or  we  do  not  Judge,  if  we  do  Judge, 
we  Judge  something  positive;  we  assert  a  relation  r,  whether 
the  relation  is  mainly  one  of  identity  or  mainly  one  of  differ- 
ence. If  wr  do  not  Judge,  that  may  represent  a  failure  of 
ours,  ne  must  not  confuse  ourselves  by  calling  it  nega- 

tion or  negative  judgment— tor  it  is  not  Judgment  at  ail, 
neither  afBrmatlon  nor  negation.  "When  we  think,"  asks 
Socrates,  "do  we  think  something,  or  nothing?"  "Some- 
thing," is  the  answer.  "And  to  think  nothing  means,  not  to 
think."i 

is  Negation  Indefinite?— Negation,  then,  is  objective  in  its 
reference.  But  there  remains  a  further  dlfBculty.  When  a 
scientist  states  that  his  results  are  "only  negative,"  he  is 
usually  not  satisfied.  Negative  conclusions  do  have  an  objec- 
tive reference,  but  It  is  felt  that  they  do  not  give  us  much 
information  about  the  object  to  which  they  refer.  "This  is 
not  Mr.  Smith"  does  not  do  much  towards  establishing  the 
identity  of  the  Unknown.  If  we  knew  him  to  be  Mr.  Jones, 
that  positive  and  affirmative  knowledge  would  of  Itself  be 
sufficient  to  rule  out  the  possibilities  of  his  being  Mr.  Smith, 
or  Mr.  Brown,  or  Mr.  Robinson.  As  we  sometimes  say,  there 
is  only  one  thing  which  a  thing  is,  but  an  infinity  of  things 
which  it  is  not.  Consequently,  to  establish  a  negative  rela- 
tion merely  touches  the  fringe  of  this  "infinity,"  and  does 
not  always  bring  us  much  closer  to  what  we  desire  to  know. 
At  best  It  does  little  more  than  narrow  the  field  of  enquiry, 
and  its  function  is  thus  mainly  preliminary  to  genuinely 
scientific  work.  It  is  for  this  reason  that  there  seemed  to  be 
some  truth  in  the  theory  of  negation  as  falling  to  get  into 
touch  with  objective  reality.  We  know  now  that  It  does  estab- 
lish contact,  but  apparently  only  with  the  fringe  or  outside 
edge  of  the  subject.  This  Is  expressed  by  saying  that  negation 
Is  indefinite — i.  e.,  Indefinite  In  not  stating  the  ground  of  the 


1  IMato,  RtpuhUc,  477  K.  fT.,  TheaetetM,  eti". 


NEGATION 


113 


nefttlon.     An  affirmative  Judgment,  It  Is  thoujht,  would  be 
more  definite,  and  would  state  the  ground  of  the  affirmation. 
Consider    the    following    InBtancea:     "Thla  watch    U    not 
going,"  "He  has  not  arrived."   'Your  letter  did  not  reach  mo," 
•She  was  not  there,"  "The  medicine  had  no  effect,"  "These 
cartridges  did  not  explode."  "Your  orders  can  not  be  carried 
out,"  "He  did  not  take  the  examlna..jn."     In  each  of  these 
(•8868  the  negation  Is  objective  In  Uh  reference,  and  la  Impor- 
tant.    It  establishes  the  fact  that  something  Is  wrong.     But 
It  leaves  It  an  open  question  as  to  what  Is  wrong.    It  Is  nec- 
essary to  search  further  for  the  ground.     Some  spring  may 
be  broken,  one  of  the  screws  may  be  missing,  the  watch  may 
require  to  be  oiled,  or  I  may  merely  have  forgotten  to  wind  It. 
He  may  have  gone  astray,  his  train  may  be  late,  he  may  have 
missed  his  train,  he  may  have  forgotten  to  start,  he  may  have 
decided  to  stay  away  and  break  the  appointment.     The  fact 
is  established,  but  the  .  xplanation  of  the  fact  Is  still  to  seek. 
Let  us  examine  further.     The  watch  is  not  going— yet  the 
springs  are  not  broken,  the  screws  are  not  out  of  place,  It 
has    not    run    down    and    remained    unwound— perhaps    the 
reason  Is  to  be  found  in  the  fact  that  it  has  not  been  oiled  for 
many  years.     So  too  the  automoblllst.  In  searching  for  the 
causa  man  when  his  machine  will   not  work,  goes  through 
such  Judgments  as  "No,  there  is  nothing  wrong  with  the 
carburetor,   nothing   Is  wrong   with   the  oU-feed.  nothing  is 
wrong  with  ih^  Ignition."  etc.,  until  Anally  he  discovers  "There 
is  no  gasoliu.,.-      Every  successive  negation  established  nar- 
rows the  field  of  enquiry,  until  at  last— we  have  the  reason, 
or  at  least  enough  of  the  reason  for  our  immediate  purposes! 
The  watch  does  not  go  because  it  has  not  been  oiled,  the 
automobile  refuses  to  move  because  there  is  no  gasoline,  the 
letter  failed  to  reach  me  because  it  did  not  leave  the  writer's 
pocket,  he  did  not  take  the  examination  because  he  was  not 
prepared. 

These  instances,  however,  prove  more  than  we  were  antici- 
pating. The  Judgments  which  actually  do  express  the  ground 
(the  watch  has  not  been  oiled,  he  was  not  prepared  for  his 
examination,  etc.,)  are  not  affirmative  but  negative.  A  nega- 
tive Judgment  can,  then,  after  all  express  the  ground.  Or— to 
state  our  result  In  another  form— negation  is  not  confined  to 
the  "fringe"  of  a  question.    V.  can  go  straight  to  the  heart  of 


114 


APPENDIX 


the  matter.  "This  coat  will  not  do,  because  there  is  not  a 
button  In  place,"  "This  composition  receives  the  mark  F, 
because  there  is  no  unity  and  no  mass  In  it,"  "He  missed 
every  shot,  because  he  did  not  understand  how  to  use  the 
sighting  apparatus."  In  other  words,  negative  Judgments  can 
be  perfectly  definite  and  explicit  in  stating  the  ground.  "No, 
I  won't  lend  you  a  dollar.  Why?— Because  you  do  not  pay 
back  what  you  borrow.'  "You  can't  thread  that  needle— the 
eye  is  not  large  enough  for  the  thread."  It  is  difficult  even 
to  imagine  more  explicit  statements  of  the  ground. 

It  is  not,  then,  impossible  for  a  negative  judgment  to  be 
perfectly  definite.  What  are  we  to  say  about  affirmative  judg- 
ments? Is  it  Impossible  for  them  to  be  indefinite?  Must  they, 
one  and  all,  state  a  ground  clearly  and  unambiguously,  or  do 
they  also  vary  from  indeuuMeness  to  definiteness?  Is  it  only 
negative  judgments  •  tiinh  dkirt  the  edge  of  a  subject  and 
gradually  narrow  it  (  ■?>  ■?  is  not  the  same  true  of  affirma- 
tive  judgments   also"; 

Let  us  consider  a  few  instances.  "There  is  a  department  of 
study  called  philosophy.  There  is  a  part  of  philosophy  called 
logic.  A  certain  part  of  logic  is  called  the  theory  of  Judgment. 
A  certain  part  of  the  theory  of  Judgment  deals  with  intellectual 
star  -.ards.  Identity  is  one  of  these  intellectual  standards." 
Here  we  have  affirmative  judgments  which  progressively  nar- 
row down  a  field  of  enquiry.  It  might,  however,  be  questioned 
whether  any  of  them  could  be  called  "indefinite."  Let  us  pro- 
ceed, therefore,  to  consldpr  a  different  type:  "Pyrrhus,  I  say 
the  Romans  can  subdue."  "A  man,  whose  last  name  began  with 
B,  called  to  see  you,"  "He  was  traveling  In  Germany,  or  some 
such  country,  at  the  time,"  "Someone  has  been  here,"  "There 
are  times  when  I  sort  of  wonder  whether  anything  is  worth 
while,"  "I  feel  something,  but  it  seems  rather  hazy."  It  is 
unnecessary  to  multiply  instances.  The  conclusion  is  simply 
forced  upon  us,  that  affirmatlvo  Judgments  also  can  be  indef- 
inite. 

We  should,  perhaps,  note  further  that  many  Judgments  can 
be  expressed  easily  and  naturally  In  either  affirmative  or 
negative  form.  The  emphasis  shifts  as  the  form  changes,  but 
the  general  meaning  seems  to  remain  much  the  same.  "Don't 
lend  him  money— he  is  not  to  be  trusted  In  money  matters." 
The  general  meaning  is  much  the  same  if  we  are  told  "he 
Is  untrustworthy  In  money  matters."    Let  us  consider  further 


NEGATION 


115 


nstances:    "The  patient  is  not  y3t  strong  enough-the  patient 
is  still  too  weak."  "This  coat  is  not  long  enough  in  the  back 
-this  coat  is  too  short  in  the  back."  "He  is  not  feeling  well 
-he  is  feeling  ill,"    "i  shall  not  be  here  tomorrow-I  shall 
be  elsewhere  tomorrow."  "That  Is  not  Jones-that  is  someone 
other  than  Jones."    "This  color  is  not  purple-this  color  is 
different  from  purple."    From  such  examples  it  looks  as  tLough 
our  thought,  whether  superficial  or  profound,  whether  indef- 
inite  or    definite,    can    be   expressed   either   afBrmatively   or 
negatively.     Affirmation   emphasises   the   identity-aspect,   and 
negation  the  difference-aspect  of  our  thought.     As  we  have 
seen  above,  all  thought  has  boih  aspects.    It  seems  safest  to 
conclude,  then,  that  all  our  thinking  has  aspects  which  can 
be  best  expressed  negatively,  and  other  aspects  which  can  be 
best  expressed  affirmatively,  but  that,  as  a  matter  of  fact   all 
our  thoughts  can  be  expressed  in  either  form,  though  one  form 
will  be  more  appropriate  to  certain  situations,  and  the  other 
form  to  other  situations. 

Our  final  conclusion  is,  that  our  thought,  whether  definite 
or  indefinite,  has  an  objective  reference,  and  that  negation  la 
as  objective  and  definite  as  affirmation,  and  affirmation  is  as 
subjective  and  indefinite  as  negation-the  two  being  related 
to  one  another  as  are  Identity  and  difference  in  our  judg- 
ments.  * 

FOR  FURTHER   READING 
r  ^),  ";„  ""'"^y-    Principles    of   Logic,    pp.    109-120.      B.    Brdmann 

Sit.)    pp.  20^21,'."'  ""•"•  '•  ^■'"'''^'  "•     ^-  ^""'*^'  ^''^'*'  (3rd 

EXERCISES 

V  V     ^'*,.^*  following  judgmePts  subjective  rather  than  objective  • 
Not  a  soldier  discharged  his  farewell  shot.     This  ribbon  Is  Zirl^ 

never  apologise.     No  combination  of  yellow  and  red  will  give  blue 
This  conduct  is  not  to  be  tolerated? 

-'.  Are  the  following  Judgments  more  IndeHnlte  than  their  affirma- 
tive counterparts:  Never  say  die.  Not  another  word!  Not  a  single 
match  would  light.  Xo  educated  man  would  accept  that  statement 
Julius  Caesar  never  dreamed  of  the  New  World.  My  desk  Is  not 
oak.  This  typewriter  has  not  a  blue  ribbon.  This  e'eotrlc  light  wU 
not  work.  Nothing  venture,  nothln-r  vln.  My  father  was  nof  in  Thi 
park  at  10:15.     -3547912  Is  not  a  prime  factor'  ' 


l! 


116 


APPFNDIX 


3.  Polttt  out  the  afflrmaUve  elements  In  the  following:  No  real 
lady  would  aot  thua.     This  material  Is  not  silk.     We  shall  never  get 

Zr,,    frt"     ^  r     '"  '"**  "  P*'*'"^"  sensation.     Not  more  than  one 
man  In  fifty  will  vote  for  that  program. 

4.  Point  out  the  negative  elements  In  the  following:  That  bi 
blue.  I  .,ve  accustomed  myself  to  wearing  white  ties.  Two  plus 
two  makes  four.  Pompeius  was  known  as  "the  Great"  in  his  own 
lifetime.  lie  was  thinking  of  taking  a  walk.  The  Are  was  growing 
stronger.     We  shall  pay  you  a  visit  tomorrow. 


*-  ^ 


PART  II. 


THEORY  OF  INFERENCE 


117 


5  h  v-dt     <r  .'■« 


Itt 


V 


CHAPTER  XI 
THE    GENERAL    CHARACTERISTICS    OF    INFERENCE 

What  are  the  Mark,  of  lnference?-What  do  we  u^^der-ta^d 
by  inference  or  reasoning?     Perhaps  we  can  beat  discover 
by  examining  a  number  of  typical  instances.     "^^  mn.^^ 
is  north  of  Minneapolis,  and  Minneapolis  is  west  of  Chicago 
then  Winnipeg  must  be  northwest  of  Chicago,  and  Ch  cago 
must  be  southeast  of  Winnipeg."      "If  our  guest  tends  to  be 
gracious  when  he  has  celery  for  lunch,  let  us  ^y^"  ^«^^ 
fay  in  a  large  supply  of  celery."     "If  a  bird  in  the  hand  is 
worth  two  in  the  bush,  then  two  in  the  bush  are  worth  one  In 
the  hand,  and  It  is  still  an  open  question  which  I  ^^y  h^P^n 
to  prefer"     "If  x^+y—xy=55,  and  x-^=o,  it  follows  that 
x=10  and  y=5."    "It  Mrs.  Smith  is  my  wife's  motheMn-law. 
then-unless  my  mother  has  married  again-my  ^o^^  ";»°;« 
must  be  Smith."    "If  I  had  15.00  when  I  started  out.  and  If 
I  only  spent  10c  for  carfare  and  *3.65  for  dry  f oo^s   |  ^er- 
alnly  ought  to  have  ?1.25  left."    "If  this  piece  <>' W"«  "tmus 
paper  turns  red.  that  is  a  sure  sign  that  the  fl";«^  before  us 
is  acid."    "If  oxygen  and  hydrogen  are  combined  in  the  pro- 
nortion  of  1:2.  the  result  is  watery 

^T^ese  cases  are  all  fairly  simple.     For  the  sake  of  com 
pleteness  let  us  add  a  few  which  are  more  complex       If  tte 
Minnesota  team  beat  Wisconsin,  and  Wisconsin  beat  Chicago 
and  Chicago  beat  Illinois,  then  Minnesota  ought  to  be  ab.e  to 
beat  Illinois."    "If  potatoes  do  well  in  Jones'  garden,  and  the 
sou  in  my  garden  is  like  his.  and  these  potatoes  are  1  ke 
hose  which  did  so  well  with  him.  and  if  I  am  as  carefula 
gardener  as  Jones,  then  I  ought  to  be  able  to  raise  a  good 
crop  myself."     "If  the  batteries  are  in  working  order,  and 
he  sparking  plugs  are  all  right,  and  the  machine  ^  ^U 
oiled,  and  the  brake  is  off.  and  there  is  plenty  of  gasoltae 
then-if  I  can  only  get  this  self-starter  to  work-we  ought 
Hegln  to  move."     "If  my  testimonials  are  all  they  should 
be  and  if  I  look  at  my  best  and  am  not  nervous,  and  if  there 
^' no  other  candidate  with  better  testimonials  or  a  better 
appearance,  then  I  ought  to  get  the  position." 

119 


120    (iKXKKAI.  CHAKACTKRISTICS  OF  INFERENCE 


Dependence. — Let  us  examine  these  various  instances  to 
discover  what  they  may  have  in  common,  in  order  that  we 
may  realise,  at  least  in  a  preliminary  «ray,  what  are  the  most 
striking  characteristics  of  inference.  One  such  characteristic 
stands  out  with  especial  prominence.  In  every  case  we  notice 
an  "if  .  .  .  then,"  a  "certainty,"  or  a  "following  upon" 
which  we  may  call  "dependence."  "//  my  testimonials  .  .  . 
then  I  ought  to  be  appointed."  That  is  to  say,  the  probability 
of  my  getting  the  position  depends  upon  these  conditions,  so 
far  as  1   \v-  An  inference  thus  seems  to  be  a  kind  of 

Judgment  which  asserts  that  a  conclusion  x  depends  upon, 
or  follows  upon,  a  condition  or  premise  a,  and  the  typical 
^rm  of  inferonce  would  thus  appear  to  be  "If  a,  then  x,"  or, 
if  we  wish  to  do  justice  to  the  complexity  of  the  cases,  "If  A 
is  B.  S  is  P."i 

Dependence  then,  or  the  following  of  a  conclusion  upon  a 
premise  or  condition,  appears  to  be  one  constituent  or  char- 
acteristic of  all  inference.  Can  we  say,  it  is  the  fundamental, 
distinguishing  feature  of  inference — or  must  we  look  further? 
Let  us  consider.  Wc  have  stated  that  inference  seems  to  be 
a  kind  of  judgment  whi^li  expresses  dependence.  Can  we  con- 
7ert  this  and  say  that  a  judgment  which  expresses  dependence 
is  an  inference?  For  this  is  one  of  the  tests  of  a  good  defini- 
tion. Let  us  see.  "My  appointment  depends  upon  certain 
conditions."  "The  direction  of  Winnipeg  from  Chicago  is  con- 
nected with  the  relation  of  both  places  to  Minneapolis."  "The 
surname  of  my  son  is  definitely  related  to  that  of  my  father." 
"Water  is  HoO."  These  formulations  of  our  thought  all 
express  dependence,  some  more  clearly,  others  less  clearly. 
They  are  all,  then,  judgments  expressing  dependence  But 
are  they  quite  what  we  should  call  inferences?  Hardly.  They 
look  more  like  what  we  should  call  statements,  and  we  should 
draw  a  distinction  between  a  statement  and  an  inferred  state- 
ment, even  when  the  simple  statement  expresses  dependence. 
The  expression  of  dependence,  then,  is  not  the  chief  consti- 
tuent of  inference,  though  it  may  be  one  of  the  characteristic 
features  of  reasoning.  It  follows,  that,  for  the  discovery  of 
the  fundamental  features  of  reasoning,  we  must  look  further. 

Analytic  Expansion. — The  objection  to  the  foregoing  defini- 
tion was,  that  it  attempted  to  reduce  inference  to  a  type  of 


1  This  view  ia  repreeented  eepeclatly  In  the  work  of  Slgwert. 
bis  Logic,  Vol.  I.  chapter  ill. 


See 


ANALYTIC  EXPANSION 


121 


judgment,  whereas  it  seems    to    be    something  wider.    If  we 
compare  such  a  Judgment  as  "My  appointment  depends  on 
certain  conditions."  with  the  inference  "If  this  condition,  and 
that  condition,  and  the  other  condition,  are  all  realised,  then 
I   ought  to  be  appointed,"  we  see  at  once  that,  while  both 
express  the  same  meaning — i.  e.,  have  the  same  reference — 
the  inference  expresses  it  in  a  more  expanded  form.    It  repre- 
sents a  more  thorough-going  analysis,  as  a  result  of  which 
all  the  steps  from  which  the  conclusion  follows  are  set  in 
array  as  explicit  conditions  or  premlses.a     Let  us  take  an 
example.     "AB=BA."     The  form  of  statement  is  ^ue  same, 
whether  it  expresses  an  intuitive  judgment — i.  e.,  is  reached 
by  "simple  inspection," — or  whether  it  expresses  the  conclu- 
sion of  a  process  of  inference.     But  the  man  who  has  gone 
through  all  the  steps-"*  has  a  much  clearer  and  more  reliable 
insight  into  the  truth  of  the  statement.    He  has  not  jumped 
hastily  to  the  conclusion,  but  has  a  knowledge  which  is  firmly 
based  upon  analysis,  and  such  knowledge  has  been  tested  and 
examined,  rather  than  left  to  first  impressions.     From  this 
viewpoint  the  distinction  between  judgment  and  inference  or 
reasoned  knowledge  is  the  difference  between  what  we  call 
"feminine  intuition,"  i.  e.,  trusting  to  unanalysed  impressions, 
and  reasoned  knowledge  based  upon  methodical  analysis.*    An 
inference  is  thus  an  analytically  expanded  judgment,  and  we 
may  regard  this  characteristic  as  "analytic  expansion." 

But  if  we  accept  this  and  look  no  further,  shall  we  be  alto- 
gether satisfied?  Our  view  makes  of  inference  an  analytic 
refinement  upon  judgment,  in  such  a  way  that,  instead  of 
stating  roughly  and  in  general  terms  that  "S  is  P,"  we  have 
analysed  out  the  various  factors  Involved,  and  know  what  it 
is  in  S  and  what  it  is  in  P  which  makes  them  stand  to  one 
another  in  this  relation.  That  such  analysis  is  of  great  value 
is  beyond  question.  But,  when  all  is  said  and  done,  are  we 
not  left  just  where  we  started?  Have  we  succeeded  in  adding 
to  the  sum  of  our  knowledge  a  single  new  idea?  Our  ideas 
are  now  far  more  clear  and  distinct.  Our  knowledge  is  highly 
polished  and  clear-cut,  but— has  it  advanced  a  single  step  In 
a  direction  which  could  be  called  newf    Have  we  discovered 

2  TMs  view  Is  represented  especially  In  the  work  of  Lotze.    See  hia 
iMgU;  esp.  a  97  ff. 
8  For  the  actual  steps,  see  infra,  chapter  xxix. 
«  Cf.  B.  L.  Nettlesbip,  Lecture*  on  Plato't  Republic,  opening  lecture. 


122    GENERAL  CHARACTERISTICS  OF  INFERENCE 

anything  hitherto  unknown?    Let  us  see.  We  know  that  8  Is  P. 
and  we  know,  rather  more  than  less,  why  we  think  bo.    We 
have  made  clearer  to  ourselves  the  elements  which  together 
constitute  the  complex  8  and  the  complex  P.    But  surely  we 
knew  all  this  before;  not  so  clearly,  perhaps,  and  not  with 
such  certainty,  but  still  In  the  main  we  did  know  It— so  that 
at  the  end  we  remain  with  the  same  sum  of  knowledge  with 
which  we  started.5    Is  this  perfectly  satisfactory  as  a  account 
of  Inference?    Does  It  not  remain  a  puzzle  how  we  could  ever 
discover  whether  8  might  be  0  or  i?  or  T-or  Indeed  how  we 
ever  managed  In  the  first  place  to  hit  upon  the  Idea  that  It 
was  P?    But  briefly,  if  this  were  all.  or  even  the  most  Impor- 
tant part  of  inference,  inference  is  the  analysis  and  classifica- 
tion of  knowledge  which  we  have  somehow  managed  to  dis- 
cover by  some  other  means.    But  we  have  a  suspicion  that 
Inference  Is  a  method  of  discovery,  that  It  Is  one  of  the  means 
of  extending  the  field  of  knowledge  and  learning  something 
which  Is  new.    Can  we  justify  this  suspicion? 

Novelty.— Let  us  ask  then,  whether  a  third  characteristic 
of  Inference  is  not  that  it  leads  to  something  new,  or  adds  to 
sum  of  knowledge.    Consider  a  few  instanros.    The  Abb6  Is 
chatting  with  the  ladies.    "Ah,  ladies,  my  first  experience  In 
the  confessional  was  terrible  indeed.     My  first  penitent  was 
a  murderer!"    Soon  after,  their  host  entered  the  room.    "Well, 
ladies,  chatting  with  our  good  Abb6?    Do  you  know,  I  was 
his  very  first  penitent?"    There  can  be  no  doubt  that  the  ladles 
drew  an  inference  which  told  them  something  new  about  their 
tost— something  which  had  not  been  told  them  either  by  the 
Abb§  or  by  their  host.    The  Abb6  had  spoken  generally,  with- 
out hinting  at  any  names,  and  had  merely  emphasised  the 
horror  of  his  situation,  as  a  young  man,  on  being  brought 
into  relation  with  one  who  had  committed  so  terrible  a  crime. 
The   whole    stress   was   on   the    shock   to   his   delicate   and 

BThP  Student  of  Latin  composition  will  be  familiar  wltli  this  from 
BThe  stuaeni  oi^i^u  i--         ^^^^^  j^  ^^^  cxeroise  that  the 

S,*?pnt  tPn«e  can  be  use^  to  express  not  only  present  time,  but  «me 

?2?^  u^  h«  really  knows  little  more  than  he  dW  be'ore^e  Is, 
If  anythi^^i^e  fa/le88  certain  which  form  «' ,«£!?«!'*"  ^*teW 
l™«SCriftte  Ina  Klven  case,  as  he  has  to  choose  between  approximately 
S^SiS^^thoutr«illy' knowing  which  would  be  the  b«rt. 


NOVELTY 


123 


untraiued   nerves,  at  meeting  with  a  rea    murderer     The 
secrets  of  the  confessional  were  not  revealed,  though  there 
was  perhaps,  a  slight  indiscretion  in  speaking  of  such  thing. 
It  all     so  tol)  their  host  does  not  tell  them  that  he  is  a  crlm- 
inal     He  is  merely  emphasising  the  many  years  that  he  and 
the  Abb6  have  known  one  another.     In  fact.  ^^  'r"  ^J^J" 
very  outset  of  the  latter's    cclesiastical  career  t»iat  they  had 
become  acquainted.    The  reference  to  the  ^<^^^^'°^'^'^'^^ 
and  general-one  of  the  usual  incidents  <>'  f  «J^  ""jf  ^7^ 
and  the  whole  stress  in  on  the  many  years  in  which  he  has 
Seen  intimate  with  their  good  Abb6.    The  in'«^«"f '  ^,7;;;'-' 
certainly  leads  to  something  new-in  fact    o  a  startling  and 
shocking  discovery  about  their  host's  early  llfe.« 

Let  us  take  another  Instance.     The  new  minister    in  the 
course  of  one  of  his  first  sermons,  happens  to  mention  how 
young  he  was  when  he  served  in  the  Spanlsh-Amerlcan  war 
"I  was  only  eighteen  at  the  time."     Instantly  every  member 
0    his  congregation  puts  two  and  two  together  and  discovers 
how  old  he  is  nou;.    This  Is  ne«,  Information.    It  Is  something 
whTch  they  wished  to  know,  and  which  he  did  not  tell  them. 
He  was  merely  emphasising  the  extreme  youthfulness  of  many 
ff   "h    boys"  at  the  time  of  that  service.    His  ParlBhloner. 
however,  compare  dates  and  come  to  a  conclusion  which  is 
an  interesting  discovery  and  satisfies  their  ^io^^^y  oa  tha 
head,    inferences  of  this  general  type  are  of  v^^y  frequent 
occurrence  in  our  every-day  intercourse,  and  are  certainly  to 
be  met  with  In  science  also.     Many  great  discoveries  have 
been   made   by   a   trained   sclentlsfs  putting  two  and  two 
Sh"  m  this  way.  and  we  may  accordingly  regard  novelty 
as  at  least  an  extremely  Important  element  In  Inference.T 

Have  we.  In  this  characteristic,  discovered  the  full  nature 
of  inference?  Can  we  rest  satisfied  with  a  deAf  ^^  j  jf  ^ 
tells  us  that  inference  Is  a  form  of  reasoning  which  leads  to 
the  discovery  of  something  new?  Let  us  consider.  Assume 
that  all  inference  gives  us  knowledge  which  Is  new.  But.  we 
must  still  ask.  is  every  process  which  gives  ««  "^^  f  °j/^ 
edge  to  be  regarded  as  Inference?  A  sudden  shoot  of  pain 
win  produce  knowledge  which  Is  new-it  Informs  me  that 
I  have  the  toothache,  that  there  Is  something  wrong  with  my 

•  Cf.  Boyce.  source,  of  Beligiou,  ImiffM.  pp.  94-96.     The  ln.t«.« 
iB  from  Hlbben'8  Logic.  ,     v      *      n 

T  Cf.  3.  S.  Mill.  Sv«*em  of  Logic,  nk.  HI.  chapter  II. 


124     GKNHRAL  CHAKACTKUISTICS  OF  INFI'RKN'CE 

tooth,  and  that  perhaps  I  had  better  see  my  dentist.  The 
last  two  statements,  which  refer  to  the  cause  of  the  pain, 
and  the  way  In  which  It  could  be  removed,  would  probably 
be  considered  Inferences.  But  the  knowledge  that  I  have  a 
pain  In  my  tooth,  or  the  toothache,  while  ce-talnly  new.  would 
not  naturally  or  usually  be  called  an  Inference.  So  too  with 
all  simple  Judgments  of  perception.  "It  Is  raining,"  "How 
warm  It  Is  getting,"  "I  am  thirsty,"  "You  look  quite  pale," 
•This  tree  Is  turning  brown, '—these  judgments  and  a  hundred 
others  of  similar  type  would  usually  be  regarded  as  Judgments 
rather  than  as  Inferences,  as  we  can  realise  If  we  compare 
them  with  such  statements  as  "The  roofs  are  wet— It  must  be 
raining,"  "Look  at  the  thermometer— how  warm  It  must  be 
getting."  etc.  And  yet  they  certainly  contain  Information 
which  Is  new.  In  order  to  exhaust  the  nature  of  Inference, 
then,  we  must  look  still  further. 

Constructive  and  Systematic— Let  us  consider.     An  Infer- 
ence differs  from  a  simple  perception,  though  both  alike  may 
give   us  knowledge   which   Is  new.     In  what  precisely  does 
this  difference  consist?     Perhaps  mainly  that  In  simple  per- 
ception we  just  apprehend  what  is  forced  upon  us,  what  affects 
us   immediately    in   sensation,    whereas   In    Inference   we   go 
through  some  process  which  may,  indeed,  start  from  sensory 
data,  but  may  lead  far  beyond  what  Is  present  In  sensation. 
This  process  consists  In  Inferring  or  drawing  or  deducing  a 
conclusion   from   premises,   i.   e.,   from   previous   knowledge, 
which  may  or  may  not  be  of  an  immediately  perceptual  kind. 
In  perception  I  just  see.    In  inference,  my  thought  completes 
Itself  by   passing  through  a  more  or  less  elaborate  process 
which  gives  me  a  result  which  has  been  deduced  or  reasoned 
out,  which  follows  upon  something  else,  which  is  true  and 
certain,  if  that  from  which  it  follows  Is  true  and  certain. 
Two  or  more  previously  acquired  pieces  of  information  are 
put  together  in  such  a  way  that  they  lead  to  a  tertium  quid 
which  is  new.    That  is  to  say,  inference  is  constructive  and 
systematic.     In   the  two  premises  we  have  fragments  of  a 
potential   system.     The   process   of   inference  seems   to  con- 
sist  in    putting   together   these   fragments   so  as   to   realise 
In  our  construction  something  more  of  the  system  of  which 
they  now  form  a  part.     The  "something  more"  which  our 
construction  thus  produces  is  the  new  information  or  conclu- 
sion.   For  example,  from  an  arc  of  a  circle  we  can  construct 


SYSTKMATIC  CONSTRUCTIVKNKSS 


125 


the  reit  of  the  circle,  by  first  discovering  the  center,  and  then 
applying  the  postulate  for  circle-construction.    That  li  to  say. 
we   manipulate   the  given   material   In  accordance  with  the 
laws  of  the  particular  system,  and  thus  acquire  new  Informa- 
tion which  Is  true  within  that  system.     So  to  In  the  Infer- 
ence "If  Mrs.  Smith  U  my  wife's  mother-in-law  .     .     .,    then 
my  son's  surname  must  be  Smith."  the  conclusion  can  only 
be  reached  by  constructing  the  system  of  relations  of  con- 
sanguinity accepted  by  present  social  conventions.    So  too  In 
"If  a  —b=    (x+y)    (x  —  y),  and  o  =  x,"  It  follows  with 
mathematical  certainty— i.  c,  It  follows  with  certainty  within 
the   mathematical    system— that    h  =  y.     This   we   can   only 
discover  by  constructing  the  relevant  portions  of  the  system 
within  which  such  algebraic   relations  are  worked  out.     So 
too  the  calculation,  In  trigonometry,  of  the  distance  of  a  ship 
at  sea  Is  discovered  by  constructing  the  system  of  cosines 
and   tangents   which   is  appropriate   to   the   special   concrete 
situation.     Inference    Is   thus   constructive   and   systematic.* 
and  this  characteristic  Is  obviously  of  such  fundamental  Im- 
portance that  we  might.  In  a  preliminary  way,  define  Infer- 
ence as  the  discovery  of  new  Information  by  the  construction 
of  a  system,  or— as  Mill  graphically  expresses  It— by  arguing 
(systematically)   from  the  known  to  the  unknown.» 

Conclusion— The  General  Characterlatlc  of  Inference.— Our 
conclusion,  then,  Is  that  Inference  Is  (1)  dependent,  i.  e.,  Is  a 
matter  of  "If  .  .  •  then."  rather  than  of  simple  state- 
ment; (2)  analytically  expanded,  i.  e..  Is  reasoned  knowledge 
as  opposed  to  an  unanalysed  Impression;  (3)  novel,  i.  c, 
leads  to  a  result  which  constitutes  a  genuine  discovery  of 
something  new;  (4)  constructive  and  systematic,  i.  e.,  reaches 
its  conclusion  by  constructing  the  relevant  portions  of  a 
system  of  knowledge  which  Is  appropriate  to  the  concrete 
situation.  Put  briefly,  inference  seems  to  be  a  process  of  dis- 
covery by  constructing  an  appropriate  system. 

But  before  we  can  advance  from  this  preliminary  sketch  to 
a  final  view  of  Inference,  we  must  examine  more  In  detail 
the  four  characteristics  which  we  have  discovered.  This 
examination  will  be  the  task  of  the  succeeding  chapters. 

0  Ct  especially  Bradley,  Principles  of  Logic,  pp.  255  ff. 

9  This  is  to  be  taken  merely  «»  *  sttlkiiig  phpam|.  Cf.  |chnppe. 
ErkenntnUstheoretitchc  Logik.  p.  260.  Sljfwart  Lojrfc.  pp.  360^62. 
How  far.  if  at  all,  we  can  reason  from  the  known  to  the  unknown 
la  considered  below. 


126    GENERAL  CH.vi  aCTKRISTICS  OF  INFERENCE 
FOR  FURTHRB  RBADINO 

B.  Bo^tnquet.  Looic.  Vol.  II.  chapter  I.  P.  II.  ^^^'"'^^J't'^^l" ^1 
Logic,  pp.  2a5-l«30.  ai»0-4t1.  n.  ICrdmann.  l.oaik.  (ind  Fxllt.),  pp. 
B88-503.     J.  O.  Illbben,  Louie  I'art  I,  chapter  x. 

EXEUCI8ES 

1      romt   out  the  elem^-nt  of  dependence  In   the  following :     Yon 

TO  e  for  V  a*  captain,  and  I'll  vote  for  your  friond  It  a|.  «"  ;';«'»• 

I^t      Get  a  KocHl  I. -k  for  your  car.  unles.  you  want  to  h«re  «t  .tolen^ 

?  didn't  Klve   him  the  order,  becanne  It  .eemod  to  me  that  he  wa. 

"rifr  r  .UmL  of  analytic  e.pan.ou.n  the  following: 

If  Bhe  be  not  fair  to  me.  what  care  I  how  fair  she  be?     «  «»«  » 

^  car    I    muat   run.     Anyone  who  can   put  two  and   two   together 

^.t  realise  that  sincere  athel-m  U  a  "t""^""* J'f 'l'^'^- .     „  ,  .n«,d 

3.     rolnt  out  the  element  of  novelty  In  the  '«>^'^'"»  ..",!, 'ST: 

15  00  a  month  for  rent,  and  llO.OO  a  year  for  books,  and  '^O^OO  a 

Jear  for  dothes.  and  other  expenses  In  proportion.  I  ough    to  manage 

«n  -hont  1450  00      If  this  Is  what  education  lends  to.   Its  back  to 

the  farm  'for  mTi     If  -unflowers.  corn  «»*  mange.-wurze  ,  grow  a. 

easily  as  that.  It  ought  not  to  be  much  trouble  to  feed  poultry. 

4       "mt   out    the    elemenc    of    systematic    constructlveness    In    the 

H.°:  '„    '" '"•  wrJwUU  „,  worl..   .  .Ml.   -'»"  •»  ""P 
him  with  his. 


CHAPTER  XII 


THE     DEPENDENT    OR     HYPOTHETICAL    NATURE    OF 

INFERENCE 

Dependent  Nature  of  lnf«rene«.— Ab  we  have  seen,  In  Infer- 
ence we  draw  our  conclusion  from  preraUea.     If  *  — y  —  fl, 
and  we  know  that  y  =  -f,  It  followa  that  x  =  10.    That  li  to 
Bay,  the  truth  of  x'a  being  equal  to  10  follows  from,  or  depends 
upon,  the  truth  of  the  premises.     //  the  premises  are  cor- 
rect, then  the  conclusion  holds  good.    //  oxygen  and  hydrogen 
are   combined   In   the   proportion   of   1:2,   water   results.    In 
other  words,  the  phenomenon  called  water  results  from  our 
experiment  only  If  the  requisite  conditions  are  fulfilled,  or 
is  dependent  upon   the  fulfilling  of  those  conditions.     It  Is 
not  true  absolutely,    but    only   on    condition   of   the   correct 
proportion   being  observed.     This  characteristic  of  the  con- 
ditionedness  of  inferred  truths  Is  expressed  by  calling  them 
"hypothetical."     Water  Is  not  regarded  absolutely,  as  water, 
but  as  the  resultant  of  certain  complex  chemical  conditions. 
Music  is  not  regarded  simply  as  music,  but  as  an  effect  pro- 
duced by  the  Intermingling  of  sound-waves  In  an  order  deter- 
mined by  a  number  of  rules,  i.  e.,  as  resulting  from  the  fulfil- 
ment of  a  whole  complex  of  conditions.    So  too  Taenia  taginata 
is  not  treated  simply  as  a  certain  kind  of  worm,  but  as  a 
certain  stage  In  a  complex  series  of  life-forms,  each  of  which 
develops   under   certain    definite   conditions,   and   the   whole 
series  of  forms  can  be  brought  to  an  end  by  Interfering  with 
any  stage  where  the  conditions  admit  of  such  interference. 
Inference,  then,  is  hypothetical,  or  the  conclusion  Is  depend- 
ent on  the  fulfilment  of  certain  conditions.    Can  we  analyse 
further  this  element  of  dependence,  and  come  to  realise  in 
what  It  consists,  or  how  It  Is  constituted?    Let  us  consider 
a  few  cases.     "If  I  delay  any  longer,  I  shall  miss  the  car." 
"If  the  corn  Is  planted  too  early,  the  seeds  will  rot."     "If 
children  persist  in  snfking  their  flngers.  they  must  be  pun- 
ished."   What  is  it  that  I  really  judge  in  such  cases?    Do  I 
judge  that  I  shall  miss  the  car,  or  that  the  seeds  will  rot? 

127 


128    DEPENDENT  NATURE  OF  INFERENCE 

Hardly,  for  perhaps  I  shall  hurry,  and  .hus  not  miss  the 
car-  perhaps  the  corn  will  be  planted  later,  in  which  case 
the  seeds  will  develop  normally.  I  do  not.  then,  judge  that  I 
shall  miss  the  car.  What  is  it,  in  that  case,  which  I  do  judge? 
Do  1  judge  that  I  shall  delay  longer,  or  that  the  corn  will  be 
^. anted  too  early?  Again,  we  must  say,  this  can  hardly  be 
the  case;  for  it  may  be  otherwi=^  and  the  "if."  taken  strictly, 
leaves  it  entirely  unsettled  whether  or  no.  I  do  not,  then, 
judge  either  that  the  seeds  will  rot  or  that  they  will  not  rot. 
In  other  words.  I  make  no  simple  judgment  at  all.i  What  is 
it  that  I  do?  I  go  through  a  process  of  thought  which  is 
complex,  and  draw  a  conclusion  from  premises.  My  judg- 
ment is,  the-  seeds  will  rot  if  planted  too  early,  I  shall  miss 
the  car  if  I  >lo  not  hurry,  children  must  be  punished  tf  they 
persist  in  wrong-doing.  My  conclusion  is  thus  a  conditioned 
conclusion,  and  what  I  judge  is  essentially  the  connection  of 
premises  and  conclusion.  I  establish  a  law  of  connection— 
the  connection  of  ground  and  consequent,  or  of  cause  and 
effect.  The  dependence  of  the  hypothetical  judgment  is  thus 
the  dependence  of  consequent  upon  ground. 

Kinds  of  Dependence:  (A)  From  Cause,  (B)  From  Absence 
of  Cause.— The  dependence  is  thus  the  dependence  of  an 
effect  or  consequent  upon  a  condition.  Let  us  proceed  to  ask. 
In  what  ways  and  to  what  extent  are  consequences  depend 
ent  upon  conditions?  Let  us  take  a  few  cases.  "If  I  expose 
myself  unduly,  I  shall  catch  cold."  The  consequence  is  here 
clearly  dependent  upon  the  functioning  of  certain  general  laws 
of  health.  Suppose  the  condition  realised,  suppose  I  do  expose 
myself  unduly.  In  that  case,  so  far  as  my  knowledge  goes.a  I 
shall  certainly  catch  cold.  So  far.  so  good;  this  is  reasoning 
from  cause  to  effect.  But  let  us  now  suppose,  on  the  other 
hand,  that  the  condition  is  not  realised— suppose  I  wrap  myself 
up  carefully.  How  about  the  consequences?  Do  I,  or  do  I  not 
catch  cold?  As  we  commonly  understand  the  laws  of  health, 
it  would  follow  that,  so  far  as  cold-from-exposure  is  concerned, 
I  do  not  catch  cold.    In  other  words,  we  can.  in  .uch  cases, 

1  Tht^  vipw  In  the  tpxt  Is  opposed  to  that  of  SlRwart.  who  regards 
both  <r  craiiTe  and  ffcoi-olauso  as  expresslnR  judRinents.  »"  tU  «eems 
&lsabt"  to  tt?at  them  as  judgmentB.  since  they  are  certainly  not 

2  The  c<mnectlon  Tieie  Is  only  "empirical"— i.  e.,  a  matter  of  Imper; 


KINDS  OF  DEPENDENCE 


129 


argue  both  positively  and  negatively.    If  the  condition  is  real- 
ised, the  consequent  Is  realised,  and  If  the  condition  Is  not 
realised,  then  the  consequent  la  not  realised  either.    We  can 
argue  from  presence  or  absence  of  cause  to  presence  or  absence 
of  effect.    The  rotting  of  seed-corn,  for  Instance,  depends  upon 
the  wetness  present  In  the  soil.    If  the  soil  Is  wet,  the  seeds 
rot;   If  the  soil  Is  not  wet,  the  seeds  do  not  rot.    If  I  wait 
longer,  I  miss  the  car;  if  I  do  not  wait,  but  hurry,  I  catch 
the  car.    If  children  persist  in  wrong-doing,  they  must  be  pun- 
ished; If,  however,  they  amend  their  ways,  they  must  not  be 
punished.    If  you  work,  you  may  some  day  amount  to  some- 
thing; if  you  don't  work,  you  will  never  amount  to  anything. 
These  are  all  instances  in  which  the  connection  Is  a  matter 
of  empirical  law.    Experience  shows  that  the  connection  holds, 
as  we  say,  In  the  Ijng  run.     But  we  do  not  have  precise 
Insight  into  the  condition,  as  we  do  in  the  so-called  exact 
sciences.     Do  we,  then,  find  a  different  result  In  the  exact 
sciences?    Let  us  see.    "If  a  triangle  Is  equilateral.  It  Is  equi- 
angular."   If  it  is  not  equilateral— if,  e.  g..  It  Is  scalene— Is  It, 
or  is  it  not,  equiangular?    It  le  not  equiangular,  and  the  case 
is  similar  to  what  we  discovered  in  the  empirical  cases.    "If 
(a+b)  be  multiplied  by  (a^b),  the  result  Is  ai—hV    If,  how- 
ever, (a+b)  be  not  multiplied  by  (a—b)—lt.  e.  g.,  it  be  divided 
by  It,  or  if  It  be  multiplied  by  re— d^- the  result  Is  not  a*— 62. 
"If  32  be  added  to  57,  the  result  is  89."    If.  however,  32  be  not 
added  to  57— if,  e.  g..  it  be  subtracted  from  57,  or  be  added  to 
41— the  result  is  not  89.    In  other  words,  in  the  exact  sciences, 
as  well  as  in  our  more  empirical  thinking,  if  our  thought  suc- 
ceeds In  penetrating  to  a  law  which  holds  good,  then  we  can 
gay:- (1)  If  the  condition  is  realised,  the  consequsnt  is  real- 
ised, and  (2)  If  the  condition  is  not  realised,  neither  is  the 
consequent.    If  A  is  B,  S  is  P;  and  if  A  is  not  B,  S  is  not  P. 

(C)  From  Effect;  (D)  From  Absence  of  Effect. — ^Let  us 
consider  further.  A  relation  of  dependence  is  two-edged.  If 
A  is  in  relation  to  B,  B  is  also  in  relation  to  A.  So  far  we 
have  considered  only  what  we  can  Infer  when  the  condition  is, 
or  is  not,  realised.  Can  we,  however,  start  at  the  other  end, 
and  ask,  given  the  consequent  or  effect,  is  it  possible  to  draw 
any  safe  conclusion  about  the  ground,  or  cause?  Or  again, 
granted  that  the  consequent  or  effect  has  not  been  realised, 
can  we  Infer,  perhaps,  that  the  ground  or  cause  has  not  been 
realised?    Let  us  consider.    Suppose  I  have  caught  cold.    This 


'•-  ^<. 


>, 


"i, 


130 


DEPENDENT  NATURE  OF  INFERENCE 


Is  an  effect.  Can  It  be  Inferred— If  it  be  an  exposure^jold— 
that  I  havb  unduly  exposed  myself?  As  we  commonly  under- 
stand the  laws  of  health,  undoubtedly.  Yes.  Suppose,  on  the 
other  hand,  that  I  have  not  caught  cold.  Can  It  be  inferred 
that  I  have  not  exposed  myself?  Not  perhaps  with  the  same 
degree  of  certainty,  for  the  statement  of  the  empirical  law  In 
question  Is  not  quite  exact,  and  people  do  sometimes  expose 
themselves  without  suffering  the  consequences.  But  on  the 
whole,  my  immunity  from  colds  is  fair  evidence  that  I  have 
taken  reasonable  care  of  myself,  and  It  would  usually  be 
argued,  that  if  I  have  no  cold,  I  have  probably  not  been  expos- 
ing myself  unduly.  Let  us  consider  the  next  case.  If  the 
seeds  have  rotted,  can  we  infer  that  the  soil  has  been  wet? 
Gardeners  would  say.  Yes.  If  however,  the  seeds  do  not  rot, 
but  develop  normally,  can  we  infer  that  the  soil  was  not  wet? 
Or  at  least  not  unduly  wet?  This  seems  a  little  less  certain 
— for  the  same  reason  as  before,  viz.,  that  the  law  is  only 
empirically  and  imperfectly  known — ^but  on  the  whole  it  also 
would  be  answered  in  the  aflQrmative.  If  the  seeds  show  no 
traces  of  rot,  it  would  be  inferred  that  the  soil  had  not  been 
wet.  So  too  in  the  other  cases.  If  I  miss  the  car,  it  can  be 
inferred  that  I  delayed  too  long.  If  I  catch  it,  it  can  be 
inferred  that  I  did  not  wait  too  long.  If  the  children  have 
been  punished,  it  can  normally  be  inferred  that  they  have  been 
doing  something  which  they  ought  not  to  have  been  doing.  If 
on  the  other  hand,  they  have  not  been  punished,  that  Is  at 
least  presumptive  evidence  that  they  have  committed  no  seri- 
ous offences.  Similarly  If  a  man's  success  is  pronounced,  it 
would  usually  be  inferred  that  he  must  have  worked  hard  to 
earn  It.  If,  on  the  other  hand,  he  never  amounts  to  anything, 
it  would  as  a  rule  be  inferred  that  he  had  not  worked  hard. 

These  cases  being  all  empirical,  the  degree  of  certainty  with 
which  we  can  argue  from  consequent  to  ground,  or  from  effect 
to  cause,  varies  in  the  various  cases.  But  on  the  whole  we 
are  certainly  convinced  that  where  the  consequent  is  realised 
— where,  that  is,  we  have  an  effect— the  condition  or  cause 
must  have  been  realised  also,  than  that  where  the  effect  is 
absent  the  suspected  cause  must  also  have  been  absent.  Let 
UB  now  review  the  cases  taken  as  examples  of  exact  science. 
If  a  triangle  is  equiangular,  can  we  argue  that  it  must  be 
equilateral?  Yes,  certainly  we  can.  If,  however,  a  triangle  Is 
not  equiangular — e.  g.,  suppose  It  obtuse-angled — Is  It  to  be 


KINDS  OF  DEPENDENCE 


131 


inferred  that  it  cannot  possibly  be  equilateral?  Yes,  again, 
quite  certainly.  Let  ua  take  the  next  case.  If  the  result  of 
multiplying  (a+b)  by  a  second  factor  be  ai — ba,  can  we  infer 
that  the  second  factor  must  have  been  (a — h)  t  Yes,  certainly. 
If,  however,  the  result  was  something  else — e.  g.,  ax — jft — can 
we  infer  that  the  second  factor  was  not  (a — b)t  Most  cer- 
tainly we  can.  Our  conviction  depends  upon  our  insight  into 
the  law  in  question — the  divisor-dividend-quotient  relation — 
and  we  can  be  in  no  possible  doubt  either  in  the  poaitiv(>,  or  in 
the  negative  case.  So  too,  if  we  are  acquainted  with  the  laws 
of  addition  and  subtraction,  we  linow  that  if  32  plus  aometMng 
adds  up  to  89,  the  second  element  in  question  must  be  67,  and 
that  if  the  result  is  not  89— but  is,  e.  g.,  65— we  can  infer  with 
mathematical  certainty  that  32  has  not  been  added  to  57.  In 
other  words,  in  the  more  exact  sciences  as  well  as  in  our  more 
empirical  J:hinking,  if  our  thought  has  succeeded  in  penetrat- 
ing to  a  genuine  law  of  connection— of  ground  and  consequent, 
or  cause  and  effect — then,  if  the  consequent  or  effect  is  real- 
ised, we  can  argue  that  the  ground  or  cause  must  have  been 
realised:  and  if,  on  the  other  hand,  the  consequent  or  effect 
is  not  realised,  we  can  infer  that  the  ground  or  cause  cannot 
possibly  have  been  realised. 

Conclusion. — Ebcpressed  generally,  our  conclusion  is,  that  if 
we  are  sure  of  the  law  which  connects  A-B  and  8-P,  so  that 
we  can  say  £l's  being  P  depends  on  A's  being  B,  then  we  can 
argue  from  our  law  of  connection  in  all  the  four  ways  discov- 
ered abo\e,  viz.,  (1)  If  A  is  B,  it  follows  that  8  must  be  P;  (2) 
if  A  is  not  B,  it  follows  that  £1  cannot  be  P  (so  far  as  our 
ivnowledge  goes);  (3)  if  &Ms  P,  it  follows  that  A  must  be  B; 
(4)  if  £1  is  not  P,  it  follows  that  A  cannot  be  B.  That  is  to 
say  we  can  reason  from  ground  to  consequent,  or  from  jon- 
sequent  to  ground,  from  cause  to  effect,  or  from  effect  to  cause, 
either  positively  or  negatively,  with  reasonable  certainty — the 
degree  of  certainty  being  precisely  proportionate  to  the  degree 
of  our  insight  into  the  law  of  connection  in  question. 

Further  Consideration. — It  is  perhaps  advisable  to  dwell  fur- 
ther on  the  imperfect  cases — in  which  we  have  not  entirely 
succeeded  in  attaining  a  genuine  law  of  connection — in  order 
to  see  what  can  be  inferred  in  such  cases.  Believers  in  appa- 
ritions, for  instance,  state  as  a  hypothetical  law  that  an  abnor- 
mal event,  such  as  a  murder,  tends  to  leave  traces  of  itself  in 
the  locality — e.  g.,  in  the  form  of  vibrations  which  perma- 


132     DEPENDENT  NATURE  OF  INFERENCE 

nently  modify  the  structure  of  the  walls  or  furnltur^  that 
when  a  sensitive  person  Is  In  the  neighborhood,  these  traces 
will  affect  the  Imagination  of  such  a  person.  In  such  a  way 
that  he  will  see  a  visual  Image  or  "ghost."    The  cause  Is  here 
the  murder,  and  the  effect  Is  the  apparition.    But  compare  the 
two  lnference8:-(a)  If  a  murder  has  ^«°  f^'J"^";*'*'  *f^f 
a  sensitive  person  will  see  an  apparition,  and  (h)  If  a  sensi- 
tive person  sees  an  apparition,  then  a  correspond  ng  crime 
must  have  been  committed.     Which  of  these  two  inferences 
would  meet  with  the  wider  acceptance?    The  great  majority 
of  believers  would  feel  more  certain  of  (b)  than  of  (a),  and 
would  justify  their  belief  by  reasoning  that  an  apparition  is 
an  effect,  and  that,  since  every  effect  has  a  cause,  an  abnormal 
effect  probably  has  an  abnormal  cause.    In  such  cases  the  argu- 
ment from  effect  to  suspected  cause  has  more  weight  than 
the  argument  from  cause  to  effect.    Let  us  now  consider  the 
negative  sJde  of  the  relation,    (c)  If  no  murder  has  been  com- 
mitted.  the  sensitive  person  will  see  no  apparition;    (d)ll 
the  sensitive  person  sees  no  apparition,  then  no  murder  has 
been  committed.     Which  of  these  two  Inferences  seems  the 
more  probable?     To  a  majority  of  the  "a"tb«f  *««    »°  J^^" 
field    (c)  would  seem  more  reasonable  than  (d).    Tnai  is  lo 
say  'm  such  cases  we  could  argue  from  the  absence  of  the 
cause  to  the  absence  of  its  suspected  effect,  but  could  not  so 
certainly  infer  from  the  absence  of  the  effect  to  the  absence 
of  the  suspected  cause. 

Let  us  take  another  instance  of  such  Imperfectly  analysed 
thought.     In  the  case  of  certain  diseases,  it  Is  believed  by 
physicians  that  If  che  patient  is  to  recover,  ^e  must  desire  to 
get  well    The  suspected  cause  Is  here  the  "will"  of  the  patient, 
and  the  effect  hoped  for  is  his  recovery.    Let  us  see  what  can 
be  inferred,     (a)  If  he  earnestly  desires  to  get  well,  he  may 
be  cured,    (b)  If  he  is  cured,  he  must  have  wanted  to  recover 
(c)  If  he  does  not  wish  to  get  well,  he  will  not  recover,  but 
will  probably  die.     (d)  If  he  does  not  recover-or  If  he  dies 
-that  is  a  proof  that  he  cannot  have  really  desired  to  recover. 
Not  one  of  these  Inferences  is  certain,  but    (a)    would  he 
thought  slightly  more  probable  than  (b).  and  (c)  would  he 
thought  slightly  more  probable  than  (d).    That  »»  *<>  "^  V" 
such  cases  as  this,  the  argument  from  cause  to  effect  seem, 
more  probable  than  from  effect  to  suspected  cause,  whether 
we  are  reasoning  positively  or  negatively.    It  Is,  however,  only 


CONCLUSION 


131 


fair  to  add  that  no  physician  would  risk  His  reputation  by  sup- 
porting any  one  ol  these  inferences.  The  probability,  in  such 
cases.  Is  usually  realised  after  the  event. 

Conclu.lon.-lB  there  any  one  inlalllble  rule  for  inferring  In 
this  fleld-the  field  of  "popular."  half-analysed  thought?    Let 
us  see.    In  the  apparition  case,  it  seemed  reasonable  to  infer 
from  the  presence  of  the  effect,  or  from  the  absence  of  the 
cause      In  the  mental  healing  case,  it  seemed  allowable  to 
argue  from  the  presence,  or  from  the  absence,  of  the  cause. 
but  not  from  tlu,  presence  of  the  effect.    That  is  to  say.  both 
cases  agree  in  permitting  an  inference  from  the  absence  of 
the  suspected  cause  to  the  absence  of  the  suspected  effect^ 
These  instances  thus  agree  with  the  seed-corn  and  car-catch  ng 
cases,  at  least  in  the  single  particular  of  admitting  an  in  er- 
ence  from  the  absence  of  the  cause.     Arguments  '"n^   <\) 
presence  of  cause.  (2)  presence  of  effect.  (3)  absence  of  effect, 
appear  to  be  admissible  in  certain  cases,  inadmissible  in  others. 
That  is  to  say.  the  only  inference  v/hich  holds  good  invariably 
in  the  instances  before  us  is  the  argument  froi-  absence  of 
cause     Can  we  then  state  as  our  conclusion  that  in  such  half- 
analysed  thought  it  is  at  least  always  permissible  to  argue 
from  the  absence  of  the  cause  to  the  absence  «' the  suspected 
effect?    Let  us  consider  yet  another  instance.    "If  Jh« /o^^r: 
tlve  ran  over  him.  he  must  be  injured,  perhaps  fatally.      What 
kinds  of  inference  can  here  be  drawn?     (1)  From  absence  of 
effect-  if  he  is  uninjured,  it  is  scarcely  credible  that  the  loco- 
motive can  have  run  over  him.     (2)  From  presence  of  cause? 
Yes.  with  a  fair  degree  of  certainty.    If  the  l<>co°^o"ve  has 
run  over  him.  we  are  pretty  sure  that  he  cannot  possibly  be 
uninjured.     (3)  From  presence  of  effect?    Let  us  see.    If  by 
'injured,  perhaps  fatally"  we  refer  (as  of  course  we  do)  to 
tlie  kind  of  injuries  received  in  being  run  over,  the  experts  at 
the  inquest  would  Infer  from  effect  to  cause,  and  their  infer- 
ence would  tend  to  be  accepted.     (4)  Finally,  can  we  argue 
from  absence  of  cause  to  absence  o.'  effect?    I^o^her  words 
does  this  case  agree  with  the  others  in  permitting  tbis  kind 
of  inference,  or  must  we  conclude  that  there  is  no  one  definite 
rule  applicable  to  such  reasonings?    If  the  lo«>™°"\«  ^  ^  "°* 
run  over  him.  can  we  argue  that  he  is  not  Injured  In  that  kind 
of  way'   Some  logicians-e.  g.,  John  Stuart  MlU-would  assert 
that  an  effect  may  be  produced  by  a  "plurality"  of  causes,  and 
that  from  the  absence  of  any  one  cause  we  cannot  reason  to 


134     DEPENDENT  NATURE  OF  INFERENCE 

the  absence  of  the  effect.     For  the  effect  might  have  been 
brought  about  quand  mime,  by  any  one  of  the  other  possible 
causes.    For  Instance,  he  may  have  escaped  the  locomotive,  but 
may  have  fallen  beneath  a  street-car  or  an  automobile.     Is 
this  objection  to  be  taken  seriously?    Or  is  it  not  rather  too 
superficial  to  merit  attention  at  the  present  day?    We  do  not 
infer  from  his  not  having  been  run  over  by  the  locomotive 
that  he  is.  e.  g.,  alive  and  well  at  the  present  moment.    That 
would  be  to  go  far  beyond  our  information.    We  argue  only 
that  he  has  escaped  injury  of  a  particular  kind— the  kind 
caused  by  locomotives.     He  has  escaped  locomotive-injuries. 
About  theoretically  possible  injuries  from  other  sources  not  a 
word  has  been  s:  id.     Qur^oncluBlon,  then,  la-that  however 
the  admissibility  of  the  other  modes  of  inference  mai_^vary  in 
empirical  cases  of  cause-effect  reasoning,  the  argument  from 
absence  of  cause  to  absence  of  effect  is  reasonable,  and  fur- 
ther, that  there  is  a  tendency  for  us  to  feel,  in  all  such  cases, 
that  if  the  connection  in  question  is  at  all  valid,  there  must 
be  some  degree  of  evidence  for  all  four  modes  of  Inference. 

Hypothetical  Versus  Categorical.— One  further  point  remains 
to  be  discussed.    Inference,  as  we  have  seen,  is  hypothetical, 
conditioned— t.  e.,  has  an  "if"  in  it.    It  might  be  thought  that 
an    unconditional    form   of   statement— "categorical"  as  It  is 
named--t.  e.,  a  direct  statement  without  even  the  suggestion 
of  an  "if"  about  It— would  be  more  valuable,  and  thus  should 
be  the  goal  of  Inference.    Compare,  for  example,  the  two  forms 
of  expression:— (1)  "//  that  street-car  coming  round  the  cor- 
ner is  yours,  you  must  hurry."    (2)  "That  street-car  is  yours; 
hurry!"    There  is  no  i/-ne8s  about  the  second,  or  categorical, 
form  of  expression.     It  is  unhypothetical,  does  not  admit  of 
doubt  or  hesitation,  but  demands  Instant  action.     The  hypo- 
thetical form  does  not  tell  us  whether  or  no— It  leaves  the  if 
in  full  force,  i.  e.,  it  leaves  the  question  still  open     The  cate- 
gorical form,  on  the  contrary,  leaves  no  room  whatever  for 
questioning  or  deliberation.    It  tells  us  outright  that  the  fact 
is  so.    It  thus  seems  to  go  further  than  the  hypothetical  form, 
and  it  might  reasonably  enough  be  asked,  which  form  should 
be  our  Ideal,  and  which  attitude  it  Is,  on  the  whole,  wiser  and 
more  logical  to  cultivate,— the  hypothetical,  or  the  categorical. 
Let  us  consider  a  little  further.    The  categorical  form  really 
seems  to  have  more  to  offer  than  the  hypothetical.     For  It 
does  not  end  with  an  unanswered  question,  but  is  direct  and 


HYPOTHETICAL  VS.  CATEGORICAL 


(35 


straight-forward,  and.  as  we  have  .eeii.  leads  Immediately  and 
by  the  flhortest  path  to  action.    It  resembles  the  bedside  man- 
ner of  the  practising  physician,  which  cuts  across  half  a  hun- 
dred hesitations  and  disputed  questions  and  boldly  orders  a 
definite  line  of  treatment.    It  la.  In  fact,  In  general,  the  atU- 
tude  of  applied  science  and  common  sense,  and,  like  them, 
betrays  a  certain  Impatience  with  the  questionings,  with  the 
sceptical.  Impartial,  judicial  attitude  of  the  theoretician,  the 
"pure"  scientist.    Practical  life  needs  quick  decisions.    Ques- 
tions must  be  settled,  one  way  or  the  other,  and  settled  at 
once.    Theory  Is  all  right  In  Its  place-but  Its  place  Is  the 
research  laboratory  or  the  research  publication,  and  not  In 
the  office  or  the  home.     What  the  practical  man  needs  is 
results,  definite  concrete  rules  which  can  be  used,  and  not 
eternal  questionings  which  lead  nowhere. 

On  the  other  hand,  the  practical  attitude  seems  somewhat 
dogmatic     To  cut  short  deliberation  and  enquiry  Is,  In  the 
last  resort,  unprogressive.  and  leads  to  mental  stagnation 
The  hypothetical  attitude  Is  concerned  with  discovery,  with 
the  establishment  of  laws,  with  the  exact  analysis  of  phe- 
nomena and  study  of  their  conditions..    Not  unduly  under  the 
Influence  of  practical  considerations,  Its  interest  Is  In  enquiry, 
m  testing,  Investigating,  finding  out  what  Is  to  be  learnt  In 
the  sure  school  of  a  science  based  upon  experience.    Not  leap- 
ing to  conclusions,  but  studying  problems;  not  deciding  too 
soon,  but  weighing  arguments;  not  rapid,  but  very  sure,  and 
above  all.  progressive.    It  Is  the  attitude  of  theory,  of  study 
and  science,  of  logic  and  philosophy,  as  opposed  to  mere  com- 
mon sense  and  an  Interest  confined  to  the  Immediate  needs^ 


fl^ 


Of  practical  living.  Which  attitude  should  be  cultivated 
depends  upon  our  character-on  the  kind  of  persons  we  are^ 
and  the  kind  of  persons  we  wish  to  be.  For  modern  logic, 
the  hypothetical  Interest  In  scientific  method  seems  more  vai 
uable  than  the  categorical,  rule-of-thumb  method  of  the  half- 
trained  practitioner,  though  It  Is  not  denied  that.  In  its  place, 
this  too  Is  valuable.  Method  versus  results;  deliberation  ver 
sus  action;  progresslveness  versus  complacency.  Which  Is  the 
more  valuable?    Which  attitude  do  we  ourselves  choose? 

concluding  Summary.-Let  us  now  put  together  what  we 
have  discovered  in  the  present  chapter.  There  are,  generally 
speaking,  two  kinds  of  knowledge :-(l)  scientific.  In  which 
we  have  attained  a  degree  of  Insight  Into  the  working  of  some 


AJ 


136 


DEPENDENT  NATURE  OF  INFERENCE 


law;  (2)  popular  knowledge,  the  field  of  the  practical  man 
with  his  rule-of-thumb  methods  and  bia  love  of  categorical 
statements.  The  first  kind  is  more  hypothetical,  and  is  inter- 
ested in  discovering  the  particular  ifs  upon  which  certain  con- 
clusions depend.  The  second  kind  does  sometimes  throw  Its 
results  into  the  if  form,  but  is  usually  more  categorical.  In 
the  hypothetical  cases,  if  we  have  succeeded  in  discovering 
some  law,  we  can  argue  or  infer  from  the  law  In  four  typical 
ways.  We  can  reason  from  the  presence  or  absence  of  the 
cause  or  ground  to  the  presence  or  absence  of  the  effect  or 
consequent;  or,  vice  versa,  we  can  argue  from  the  presence 
or  absence  of  the  consequent  or  effect  to  the  presence  or 
absence  of  the  ground  or  cause.  If  our  thought  has  only  par- 
tially succeeded  in  its  analysis,  and  we  are  not  quite  certain 
of  our  suggested  law,  we  cannot  argue  with  the  same  de,  ree 
of  certainty.  The  ideal  is,  here  also,  all  four  forms  of  Infer- 
ence, but  In  practice  we  have  found  only  one  which  does  not 
vary — viz.,  the  argument  from  the  absence  of  the  cause  to  the 
absence  of  the  effect.  This  has  seemed  always  reasonably 
admissible,  but  In  proportion  as  our  knowledge  is  greater  and 
our  thought  more  strict,  even  the  popular  forms  of  inference 
tend  to  allow  all  four  types  of  reasoning.s 

SA8  a  practical  UluBtratlon  of  what  we  have  discovered  In  the 
Dresent  chapter,  we  might  state  that  If  It  Is  true  that  the  worKlngs  or 
a  law  lend  themselves  to  the  four  typical  Inferential  forms,  then  It 
win  also  be  true  that  wherever  we  can  make  all  four  Inferences  with 
reasonable  certainty,  that  la  a  safe  test  of  the  validity  of  the  law  In 
ouestlon,  and  that  where  we  are  unable  to  draw  all  four  Inferences 
with  equal  certainty,  that  U  a  safe  Indication  that  we  have  not  yet 
succeeded  in  discovering  the  law  In  the  case  In  question.  Cf.  the 
rule  re  the  convertibility  of  a  definition,  infra,  chapter  xxvll. 

FOR  FURTHBB  RBADINQ 

F.  H.  Bradley,  Principle*  of  Logic,  Bk.  I,  chapter  U.  J.  O.  Hlbben, 
Logic,  Part  II,  chapter  xll.     Chr.  Slgwart,  Logic.  Vol.  I,  pp.  326-338. 


BXERCI8BS 

1.  Assuming  the  following  Inferences  to  be  correct,  what  Infer- 
ences can  be  drawn  from  ground  to  consequent,  or  from  consequent 
to  ground,*  and  which  of  these  seem  the  more  probable :  If  he  writes 
to  me  again,  I  shall  not  read  hU  letter.  If  the  tewn-mower  won't 
cut,  I  Bhall  send  and  have  it  sharpened.  If  the  car  has  no  gasoline, 
of  course  It  won't  sUrt.  If  this  sand  were  only  cleared  away.  It 
would  be  grand.  If  you  want  to  be  an  engineer,  you  will  bar*  to 
■tudy  and  go  to  college? 


EXERCISES 


137 


2.  Asraming  the  following  taferenvei  to  be  correct,  what  Infer- 
ences can  be  drawn  from  ground  to  consequent,  or  from  consequent 
to  ground:*  If  you  will  not  help  me  put  the  car  Into  the  garage, 
I  shall  not  take  you  out  riding  with  me  again.  If  this  lilstory  book 
says  BO,  It  must  be  true.  If  the  engine  Is  really  off  the  rails.  It  will 
be  necessary  to  get  a  derrick  for  It.  If  you  lore  me,  you  will  loTe 
my  dog.     If  you  are  a  good  shot,  you  should  score  100%   at  that 

range?  ,.  ^   .  , 

3.  Assuming  the  following  Inferences  to  be  correct,  what  inier- 
ences  can  be  drawn  from  ground  to  consequent,  or  from  consequent 
to  ground  :*  If  x  =  5  In  the  equation  2x  —  8xy  +  4y  =  10,  then 
y  =  1.  If  the  plane  figure  In  question  l«  such  that  It  la  rectilineal, 
and  a  closed  figure,  and  such  that  any  of  Its  exterior  angles  Is  equal 
to  the  sum  of  the  Interior  opposite  angles,  the  figure  In  question 
must  be  a  triangle.  If  the  quotient  Is  61,  and  the  (Mvldend  Is  SOS. 
the  divisor  must  have  been  5. 

*{.  e.,  both  from  the  presence  of  ground  (or  consequent),  or  from 
the  absence  of  ground  (or  consequent). 


CHAPTER  XllI 


THE  ANALYTICAL  CHARACTER  OF  INFERENCE 


Iv 


Nature  of  Analysit.— So  far  we  have  considered  the  differ- 
ence between  the  categorical  and  hypothetical  viewpoints,  and 
have  seen  that  Inference  or  reasoning  is  hypothetical  rather 
than  categorical.  Let  us  now  proceed  to  compare  statements 
and  Inferences  from  a  new  viewpoint,  In  order  to  bring  out 
what  we  took  to  be  the  second  main  characteristic  of  infer- 
ence, viz.,  its  analytical  nature. 

The  practical  man  never  analyses,  If  he  can  help  it.^  He 
just  acts,  and  acts  in  accordance  with  habit  and  routine.  For 
most  of  the  purposes  of  life— which  are  instinctive — little 
analytical  reasoning  Is  required.  Most  of  our  ends  are  easily 
attained,  and  a  conventional  attitude  of  mind  as  well  as  a 
conventional  appearance — what  we  call  the  professional  man- 
ner— carries  us  safely  through  most  of  the  social  contingen- 
cies which  present  themselves.  It  is,  in  fact,  only  when  things 
cease  to  run  smoothly,  when  something  goes  wrong,  that 
analytical  thought  is  called  into  play.  A  man  who  finds  the 
door  refuse  to  open  behaves,  at  first,  precisely  like  a  trapped 
animal,  such  as  a  dog,  cat,  or  monkey.  He  pulls,  pushes,  kicks, 
and  knocks,  and  makes  a  fuss  generally.  It  is  only  when  this 
method  fails  that  his  attention  Is  directed  to  investigating  the 
cause,  and  to  taking  measures  to  have  the  conditions  reme- 
died— e.  g.,  by  telephoning  to  the  janitor  or  locksmith,  before 
descending  by  way  of  the  fire-escape  or  window.  The  occasion 
for  inference  is  thus  the  breaking  down  of  our  customary 
methods  of  procedure  before  novel  circumstances.  These  neces- 
sitate the  adoption  of  new  methods  especially  adapted  to  the 
new  occasion — require  a  new  analysis  of  the  situation,  a  sub- 
stitution of  analytical  Investigation  for  the  practical  rule-of- 
thumb  method  of  "common"  sense. 

So  much  for  the  occasion  of  Inference.    The  way  In  which 
we  actually  reach  our  solution  is  still,  in  the  main,  the  method 

1  Cf.  W.  B.  PllUbury,  FundamentaU  of  Psychology,  chapter  xi  (on 
Reasoning) . 


138 


NATURE  OF  ANALYSIS 


139 


of  trial  aud  error.  Various  associations  are  aroused,  tested 
mentally,  and  rejected,  until  at  last  there  comes  Into  our  minds 
one  which  flts  the  case  and  leads  to  action.  Explicit  analysis 
takes  place  only  when  we  direct  our  attention  to  the  chief 
elements  in  the  problem,  and  to  the  chief  steps  of  a  solution 
which  will  be  Just  to  them  all. 

In  this  way,  then,  we  analyse  practically  a  practical  situa- 
tion.   Let  us  proceed  to  consider  a  case  which  Is  less  imme- 
diately practical.    I  am  reading  Kant's  "Critique  of  Pure  Rea- 
son," and  am  doing  my  best  to  understand  the  "psychological" 
part  of  the  "transcendental  analytic."    I  find  that  a  great  deal 
of  the  constructive  work  of  knowledge  is  performed  by  the 
'imagination,"  but  when  I  try  to  make  clear  to  myself  Just 
what  imagination  does,  especially  as  compared  with  sense  on 
the  one  hand  and  understanding  on  the  other,  I  find  myself 
baffled.    I  try  all  the  ways  out  which  suggest  themselves.    Has 
imagination,  In  Kant's  sense,  anything  to  do  with  mental 
imagery? — That  doesn't  seem   to   fit  in  with  its  "transcen- 
dental" functions.    Is  it,  perhaps,  like  the  creative  Imagination 
of  the  poet? — That  also  does  not  seem  very  helpful.    I  consult 
the  explanatory  literature  which  Is  at  my  disposal — but  that 
seems  to  play  fast  and  loose.    At  one  moment  Imagination 
seems  the  same  as  sensory  perception,  at  another  It  exercises 
much  the  same  functions  as  understanding— with  the  peculiar 
qualification  that  it  is  "blind."    I  give  up  this  way  of  trying 
to  learn.    Unmethodical  guesses,  or  looking  up,  at  haphasard, 
literature  which  was  obviously  written  without  any  feeling 
for  my  particular  problem,  gets  me  nowhere.    I  decide  to  find 
out  for  myself,  if  possible.    There  Is  only  one  way  to  find  out, 
and  that  is,  by  exhaustive  analysis  of  the  situation  itself.    I 
make  a  collection  of  all  the  passages  in  which  the  term  Is 
used.     I  then  collect  leading  statements  about  sensory  expe- 
rience, and  about  the  work  of  understanding.     I  proceed  to 
classify  the  data  with  which  I  have  thus  furnished  myself, 
putting  together  all  statements  which  seem  to  bear  on  some 
one  point— c.  g.,     (1)  the  "blindness"  of  imagination,  (2)  its 
"synthetic"  function,  (3)  the  relation  of  reproductive  to  pro- 
ductive  imagination,   (4)    "schemata"  as  distinguished  from 
images,  etc.— nntW  I  have  exhausted  all  the  distinguishable 
points  which  appear  to  be  treated  in  Kant's  writings.    I  then, 
very  gradually,  find  what  he  seems  to  have  had  in  mind,  and 
my  problem  is  solved. 


w 


140      ANALYTICAL  CHARACTER  OF  INFERENCE 

Here  again,  although  the  material  ia  very  different,  the  gen- 
eral method  of  dealing  with  the  situation  seemi  much  the 
fame  aa  before.  I  do  not  analyse  until  the  rough  and  ready 
method  of  trial  and  error  breaks  down.  Here  also  my  analysis 
seems  to  be  simply  an  attempt  to  appreciate,  one  by  one,  the 
various  distinguishable  features  of  the  situation,  ir  the  hope 
that.  If  I  take  them  one  at  a  time,  some  ray  of  Illumination 
may  dawn  upon  me,  and  I  suall  be  helped  out  of  my  diffi- 
culty. It  differs,  however,  from  the  old  attempt  by  being 
methodical  and  exhaustive,  rather  than  haphazard  and  at  ran- 
dom. It  tries  all  the  ways,  rather  than  those  which  chance  to 
present  themselves  to  me,  and  thus  leads  to  some  sort  of  sat- 
isfaction. For  If  I  have  tried  all  the  ways,  I  know  that  I  have 
done  my  best,  and  that  my  non-success  Is  not  a  mere  matter 
of  chance — which  a  little  perseverance  might  remedy. 

Special  Features  of  AnalyaJs.— Let  us  focus  our  attention  a 
little  more  closely  upon  certain  features  of  our  analytical 
method.  In  the  first  place,  we  do  not  bring  in  hypotheses  ex 
macftina.  To  find  our  solution  we  split  up  Into  Its  elements 
the  situation  which  Is  before  us,  and  act  accordingly.  If  I 
wish  to  learn  to  play  music,  it  will  never  do  Just  to  read  books 
on  "the  three  B's,"  Bach,  Beethoven,  and  Brahms,  but  I  must 
patiently  and  methodically  practise  scales,  chords,  ana  pas- 
sages, until  I  can  solve  the  technical  problems  presented  in 
the  particular  aonata  or  fugue  which  I  wish  to  perform.  There 
are  also  musical  problems  to  be  solved,  which  also  will  require 
specialised  studies  appropriate  to  the  occasion.  We  have  to 
remain  very  close  to  our  data.  Thus  no  one  would  dream  of 
Inferring  that  Socrates  must  die  on  the  general  ground  that 
"all  men  are  mortal,"  but  for  the  specific  reasons  that  the 
Athenians  have  condemned  him  to  death,  that  he  Is  In  the 
condemned  cell,  that  the  fatal  morning  has  arrived,  that  he  has, 
in  fact,  drunk  the  hemlock  and  It  has  begun  to  take  effect.  So 
too  no  botanist  would  infer  that  plauta  grow  upwards  because 
they  love  the  sun,  or  even  because  they  have  a  positive  hello- 
troplsm  and  negative  geotroplsm,  but  would  dissect  the  various 
stem-cells,  and  would  show  the  precise  way  In  which  certain 
starch-granules  rest  normally  upon  the  sensitive  protoplasm  at 
the  bottom  of  those  cells,  and  thus  furnish  a  delicate  mech- 
anism for  appreciating  the  Influence  of  gravitation,  analogous 
to  the  statocysts  of  primitive  animals.    So  too  the  X-chromo- 


SPECIAl     FEATURES  OF  ANALYSIS 


141 


■omfl  and  the  mitotic  subcUvMon  of  cells  w«r«  dltcoTared,  not 
by  general  reaMntoKM,  or  by  baphasard  gueMes,  bat  by  pattest 
and  methodical  exptirimeaitattoB  with  the  vaiioua  teeter* 
shown,  by  htetolaclcal  analjrala,  to  be  present  In  the  concrete 
situation.  It  is  thus  the  ■itoation  before  ue  wlitch  la  tho 
direct  and  sole  a«bjH«'t  of  our  analysis. 

A  second  triiestlon  concerns  the  "ele-ionts"  to  wbieh  wa 
analyse.  These  vary  in  the  various  coucrete  situation.  If  we 
are  studying  language.  It  13  In  units  which  are  gramaBatieal 
or  phonetic,  that  our  analysis  terminates.  If  it  Is  plane 
geometry  that  we  are  studying,  our  analysis  terminates  In 
lines  and  points.  If  it  is  history,  then  we  end  up  with  the 
various  types  of  dosa  which  ca;^  be  regarded  as  fnralabing 
"testimony,"  whettsB-  docinnentB,  archaeological  remains,  or 
what  not.  We  do  mot  !lnd  tones  in  histological  asalysia,  or 
centrosomes  in  mawsi  analysis.  That  Is  to  say,  our  anita 
or  elements  differ  qitalltativeiy  according  to  the  qualltatlT* 
differences  of  our  variouH  universes  of  discourse.  But  In  spit* 
of  these  differences — differences  so  great  tliat  we  can  aeldom 
hope  to  argue  from  what  taken  place  in  one  field  to  what  may 
be  expected  to  happen  in  another  field — there  are  certain 
Important  respects  in  which  onr  elements  agree.  Analysis  M 
such  always  Involves  interference  with  the  concrete  situation. 
It  is  split  up.  It  ceases  to  exist  In  its  natural  form.  What  Is 
Irrelevant  for  our  purposes  in  discarded,  and  only  what  la 
strictly  to  the  point  is  taicen  into  the  focus  of  attention.  This 
involves  a  certain  artificiality,  and  our  elements  are  all 
abstract,  intellectualised  entities,  bloodless  concepts.  The  trail 
of  the  Intellect  ia  over  them  all. 

This  gives  to  the  products  of  analysis  a  certain  unity  which 
we  should  never  anticipate  from  what  we  have  seen  of  the 
qualitative  differences  of  the  various  universes  of  dtoconrse 
— a  unity  derived,  of  course,  from  the  Intellectual  nature  of 
analysis  Itself.  The  products  of  analysis  are,  for  instance, 
almost  always  numerable,  and  almost  always  parts  of  whole»; 
and  they  always  have  a  (varying)  nu»'cer  of  other  characte-- 
Istics  In  common.  From  this  unity  of  form,  it  8<»Beti»es 
comes  about  that  the  instrument!!  f^^d  by  InteUisen^i  to 
deal  with  one  type  of  situation  can,  as  a  matter  of  fact,  be 
utilised,  with  but  slight  changes,  to  deal  with  another  type  of 
situation.    Our  analytical  methods  *hos  become  schematised. 


142        iNALYTICAL  CHARACTER  OF  INFERENCE 


Just  as  the  artist  has  a  body  of  working  schemess  for  repre- 
senting a  man,  a  tree,  or  a  house.  Just  as,  in  social  Intercourse, 
we  acquire  generalised  ways  of  approaching  other  people  with 
what  we  call  "tact," — so  the  trained  scientist  has  at  his  com- 
mand a  body  of  generalised  ways  of  dealing  with  his  kind  of 
problems — a  method  of  analysis  which  can  be  applied  easily 
and  with  but  slight  modifications  to  fit  all  sorts  of  special 
cases.  A  logician  like  Bosanquets  or  Royce  can  apply  the 
schemes  of  biological  analysis  to  logic.  A  metaphysician  like 
Spinoza  can  apply  quantitative  methods  to  the  concept  of 
Deus  sive  Natuira— and  there  seems  to  be  no  way  of  deciding 
how  far  this  can  be  done.  "Transgressing  into  another  kind," 
as  Aristotle  named  it,  has  become  a  fine  art,  and,  as  a  matter 
of  actual  practice,  we  all  recognise  that  "scientific  method"  is 
much  the  same,  whatever  the  special  material  to  which  it  Is 
applied. 

A  fourth  feature  of  our  analytical  method  is,  that  it  does 
not,  and  can  not,  go  beyond  its  data.  Schematised  and  gen- 
eral as  it  is,  it  can  never  extract,  in  the  way  of  elements, 
more  than  is  present  to  be  extracted.  It  splits  up  the  con- 
fused and  concrete  situation,  omits  what  is  irrelevant,  and 
takes  up  what  is  relevant.  These  elements  stand  out  far 
more  clearly  after  the  analysis  than  before,  as  In  Aristotle's 
analysis  of  friendship,*  or  Windelband's  analysis  of  Plato.6 
But  they  were  there  all  through,  embedded  in  the  concrete 
situation,  and  only  awaiting  our  analysis  for  their  discovery. 
This  is  so  obvious,  that  it  would  be  unnecessary  to  emphasise 
It,  if  it  were  not  so  incessantly  sinned  against.  To  recon- 
struct Locke's  thought  in  the  light  of  Condillac«  or  of  KantT 


aCf.  F.  C.  Ayer,  The  Pavchology  of  Drawing,  esp.  pp.  8-0,  74-76. 
100,  169.  A  "soheme"  Is  ft  method  for  representing  In  an  Image,  as 
e.  a.,  the  method  of  representing  pleasure  or  grief  In  the  human  coun- 
tenance by  curving  the  eyos  and  mouth  upwards  or  downwards,  respec- 
tively. 

8  noMnquet's  book  Is  "Ix)glc  or  the  Morphology  of  Knowledge." 

4  See  Aristotle's  Vieomavhrnn  EthUn.  Bks.  VIII-IX,  with  the  Intro- 
duction of  Sir  Alexander  Grant  to  Ilk.  VIII. 

»  WIndelband,  In  hiR  small  volume  on  Plato,  by  treating  In  separate 
chapters  Plato  as  a  Teacher,  as  a  Philosopher,  as  a  Theologian,  as  a 
Prophet,  and  as  a  "Social  Thinker,"  has  given  an  Impression  of  amas- 
tng  lucidity — such  a-  without  that  analysU  would  nave  been  Impoa- 
Blble. 

8Cf.  c.  g.  Victor  Cousin,  La  Phllosophte  de  Loctif. 

TCf.  e.  a.  the  treatises  comparing  Locke  and  I^elbnlz  written  by 
O.  HarteuHteln  and  by  O.  v.  Kenolt — to  mention  only  two  out  of  a 
goodly  company. 


ANALYSIS  AND  INTUITION 


143 


.<*  Just  ae  Illogical  as  to  reconstnict  Kant  In  the  light  of 
Hegel,8  or  to  read  monlBtic  idealism^  or  Freudian  psychologyio 
into  Shakespeare.  The  analysis  of  Locke's  thought  should 
lead  to  elements  which  are  Locklan;  the  analysis  of  Shakes- 
peare to  elements  which  are  Shakespearean,  Just  as  the  analy- 
sis of  space  leads  to  elements  which  are  spatial,  or  of  time  to 
elements  which  are  temporal.  Otherwise  we  are  embarking 
upon  the  hopeless  quest  of  explaining  everything  in  terms  of 
something  else — i.  e.,  in  terms  of  something  which  is  not  it— 
which  is  the  reductio  ad  absurdum  of  such  explanation.  Our 
analysis  must,  then,  restrict  itself  to  what  is  given,  and  must 
not  attempt  to  read  into  Its  data  something  which  Is  extrane- 
ous and  strictly  irrelevant. 

Analysis  and  Intuition. — So  far  we  have  seen  that  the 
analytical  method,  in  splitting  up  the  given  situation.  (1) 
keeps  as  close  as  may  be  to  its  data,  (2)  is  schematic  or 
slightly  more  general  than  the  specific  occasion  seems  to 
require,  (3)  leaves  us  with  elements  which  are  somewhat 
artificial,  and  yet  (4)  were  there,  embedded  in  the  concrete  sit- 
uation, only  awaiting  methodical  analysis  to  become  evident. 
It  remains  to  compare  it  with  a  method  which  <'  iploys  no 
explicit  analysis,  but  reaches  its  conclusions  by  sin.  i  Inspec- 
tion— the  intuitive  method. 

Compare  for  example,  (1)  "His  character  must  be  good,  for 
he  has  consistently  acted  in  this,  that,  and  the  other  kind  of 
way,"  and  (2)  "His  character  is  good— I  couldn't  say  why,  but 
I  Just  feel  sure  of  him."  The  analytical  inference  is  less  cer- 
tain than  the  intuition,  less  confident  of  Itself.  It  sums  up 
the  evidence,  and  rests  the  responsibility  for  the  conclusion 
upon  the  certainty  of  that  evidence.  The  intuitive  Judgment 
says  nothing  about  the  evidence — there  is  no  appeal  to  logical 
reasoning,  for  the  person  in  question  feels  sure — ^he  "Just 
knows."  So  too  we  might  compare,  (1)  "This  way  must  be 
shorter  than  that,  for  if  you  count  up  the  number  of  blocks, 
you  will  find  that  there  are  two  more  blocks  that  way,"  and 
(2)  "This  way  Is  shorter  than  that— It  Just  seems  so  some- 
how." The  intuitive  person  seems  less  hesitant,  seems  to  feel 

*  C(.  e.  a.,  tlM  accoants  of  Ktnt  given  by  Kudo  Fischer  and  bv 
Kdward  Calrd. 

'Cf.  A.  C.  Bradley,  Shakctpcarcan  Tragedy. 

10  Cf.  Erneat  Jonea,  "The  Oedlpua-complez  aa  an  explanation  of 
Hamlet'a  nuratery,"  *»  American  Journal  of  Ptmholon,  Vol.  XXI, 
1910,  pp.  72-118,  and  PtychoanalntU. 


144      ANALYTICAL  CHARACTER  OF  INFERENCE 


less  In  need  of  the  longer  way  round  to  his  conclusion.  In 
some  cases  the  longer  way — that  of  analytic  inference— eeems 
less  applicable.  Compare,  c.  g.,  (1)  "This  pictu'-e  must  be 
finer  than  that,  for  (a)  you  can  see  what  this  is  inteuJed  for, 
(b)  it  is  drawn  according  to  the  rules  of  perspective,  and  (c) 
the  colors  are  bright  and  clear,"  with  (2)  "This  picture  is 
finer  than  that — I  couldn't  give  any  reason,  and  I  don't  need 
to— it  is  a  matter  of  the  aesthetic  intuition.  Either  you  have 
it  or  you  have  not.  If  you  have  it,  you  don't  need  to  argue 
about  It — you  just  know." 

Both  intuition  and  analysis  arrive  at  conclusions— but  only 
analysis  states  the  evidence  on  which  the  conclusion  seems  to 
depend.  Intuitive  thought  is  far  more  common  than  analysis. 
For  most  purposes  it  is  sufficiently  correct,  and  for  some  pur- 
poses— e.  g.,  in  judging  works  of  art — it  seems  more  correct. 
But  we  may  reasonably  as .,  which  of  the  two  attitudes  of 
mind  Is  it  wiser  to  cultivate?  On  the  one  hand  we  have  the 
widespread  belief  in  intuition.  "Give  your  decisions,"  said 
the  experienced  judge  to  the  new  appointee,  "they  will  prob- 
ably be  right.  But  keep  your  reasons  to  yourself— they  are 
sure  to  be  wrong."  So  too  our  modern  psychologistsu  tend  to 
regard  all  motivation  as  welling  up  out  of  the  depths  of  our 
subconscious  nature,  while  all  the  specious  reasons  which  we 
give  for  our  conduct  tend  to  be  discounted  as  mere  "ration- 
alisations," i.  e.,  as  disguises  by  which  we  hide  our  motives 
from  ourselves  and  others  by  letting  them  appear  only  as 
clothed  in  language  appropriate  to  the  system  of  ideals  recog- 
nised by  the  conventions  of  social  usage.  On  the  other  hand 
we  have  the  equally  widespread  belief  in  reflection,  analysis, 
deliberation.  To  which  of  these  two  opposed  beliefs  ought  we 
to  yield  the  more  loyal  allegiance? 

By  intuition  we  mean,  in  general,  that  attitude  of  mind  by 
which  we  put  ourselves  in  the  other  fellow's  place,  and  try  to 
feel  as  he  would  be  feeling.  It  is  a  matter  of  feeling  rather 
than  of  reasoning,  and  seems  to  be  immediate,  structureless, 
simple — just  knowing.  It  is  unreflective  and  unmethodical, 
and  feels  a  certain  distrust  of  elaborate  arguments,  as  of 
instruments  which  somehow  come  between  us  and  what  we 
are  studyng— which  distort  and  falsify  our  view,  warping  our 
Judgment  until  wc  don't  really  know  Just  what  we  do  believe. 

11  Cf.  e.  g.,  W.  James,  Varietiet  of  ReUgiova  Bteperience,  and  Bernard 
Hart,  Paychology  of  IntoMty. 


/ 


ANALYSIS  AND  INTUITION 


145 


We  feel  the  value  of  Intuition  especially  in  ethics,  in  aesthetics, 
and  above  all  in  religion.  It  is  especially  in  these  fields  that 
we  trust  our  intuitions  most  completely,  and  feel  most  distrust 
of  reasoning.  "Metaphysics,"  says  Bradley — himself  a  meta- 
physician— "is  finding  bad  reasons  for  what  we  believe  by 
instinct."t2 

On  the  other  hand,  in  mathematics,  in  chemistry.  In  biology, 
and  in  the  sciences  generally,  we  should  never  dream  of  trust- 
ing to  Intuition.  In  these  fields  analysis,  patient,  methodical 
experimentation,  with  all  the  powers  of  reasoning  as  well  as 
of  observation  which  we  possess,  is  universally  admitted  to  be 
the  only  feasible  method.  So  too  In  much  of  our  every-day 
life  we  should  never  think  of  trusting  intuition.  Do  I  have 
an  "intuition"  that  this  Is  my  street-car,  that  the  rain  will  be 
only  a  shower,  that  the  business  deal  which  I  have  Just  com- 
pleted is  going  to  turn  out  a  magnificent  success?  Yes,  I  do 
have  intuitions  in  this  field,  but  experience  has  taught  me  to 
distrust  them,  and  to  replace  them  by  analysis  and  experiment. 
Scientific  method,  in  business  as  well  as  in  purely  acientiflc 
study,  reliance  upon  analysis  and  reasonings  verified  by 
methodical  appeals  to  experience.  Is  the  only  safe  guide  here. 

What  are  we,  then,  to  conclude?  Are  we  to  believe  that  in 
practical  life  and  in  science,  analysis  should  be  our  rule,  bat 
that  in  all  which  concerns  the  inner  life, — art,  goodness,  and 
religion,— intuition — ^unanalysed  feeling— is  a  trustworthy 
guide?  There  is,  of  course,  no  doubt  t^at  this  is  precisely  the 
solution  which  most  men  accept — the  system  of  watertight 
mental  compartments — one  for  the  ofllce,  another  for  the 
church;  one  for  the  opera-house,  another  for  home  life.  In  , 
business  relations.  In  scientific  research,  they  analyse  and 
infer.  Nothing  is  taken  upon  faith.  In  the  realm  of  ideals 
and  "values,"  faith,  trust,  intuition  Is  their  guide.  We  must-^ 
ask,  however,  not  whether  this  attitude  is  commonly  accepted^ 
but  whether  it  is  wise,  consistent,  logical,  whether  it  is  not 
rather  the  source  of  our  unprogressiveness  in  the  things  of 
the  spirit,  in  the  essentials  of  civilisation,  while  in  externals 
we  seem  to  have  advanced  by  leaps  and  bounds. 

Let  us  consider.  Intuition  is  not  radically  distinct  from 
analytical  reasoning.  Both  often  reach  the  same  conclusion, 
and  often  take  a  similar  path.    The  only  difference  is,  that  for 


"Cf.   F.   II.   Bradley,   Appearance  and   RealUy,  preface. 
B.  Huaaell,  Problemt  of  PMloiophy,  pp.  30-40. 


Cf.  also 


O^"^  ^-^-t'i. 


-'  **  -     ■     /*^l 


146      ANALYTICAL  CHARACTER  OF  INFERENCE 


intuition  the  reasons  are  not  made  explicit,  are  not  weighed 
and  tested,  but  Just  followed.  All  the  emphasis  is  placed 
upon  the  conclusion — the  way  by  which  that  conclusion  has 
been  reached  remains  out  of  sight.  Our  choice,  then.  Is 
between  (1)  accepting  conclusions  with  unbounded  faith,  but 
without  careful  weighing  of  the  evidence  and  setting  forth 
the  grounds  which  might  Influence  a  reasonable  man,  and  (2) 
only  drawing  Inferences  after  the  fullest  consideration  and 
analysis  of  all  the  facts  before  us.  So  stated,  there  can  be 
no  longer  any  hesitation.  Reflective  analysis  as  a  method 
for  the  conduct  of  life  is  Immeasurably  superior  to  unreflect- 
ing intuition — wherever  and  whenever  such  analysis  can  be 
fruitfully  applied.  The  reason  why  it  has  not  been  accepted 
as  tbe  sole  reasonable  method  Is  because  the  inner  life  cannot 
easily  be  subjected  to  sclentiflc  analysis,  as  well  as  the  pres- 
sure of  practical  needs,  which  so  often  conflne  our  attention 
to  the  external  things  of  life.  But  there  can  be  no  doubt 
that,  as  our  psychological  insight  gradually  develops,  we  shall 
be  able  to  extend  the  method  of  analytical  Inference  over  more 
and  more  of  the  inner  life,  and  that  the  progressivenesb  '^.hich 
is  so  marked  a  feature  of  the  fleids  to  which  that  method  has 
hitherto  been  applied,  will  continue  to  invade  the  new  terri- 
tory also.  Wherever  applicable,  then,  analysis,  deliberation, 
weighing  all  the  evidence,  bit  by  bit,  is  a  safer  guide  than 
intuition,  and  the  reasoning,  deliberative,  analysing  habit  of 
mind  is  the  one  to  cultivate. 

Conclusion. — Our  conclusion  is,  then,  that  inference  is 
analytical,  i.  e.,  does  not  treat  the  material  before  it  as  a 
simple  unanalysable  whole,  to  be  reacted  to  by  an  intuition, 
but  as  a  complex  situation  which  must  be  split  up  into  its 
elements.  Such  Inference  remains  always  close  to  the  coti- 
creteness  of  the  situation,  and  examines  the  elements,  one  by 
one.  As  produced  by  an  analysis  which  has  torn  them  from 
their  living  context,  such  elements  are  somewhat  artificial. 
But  they  are,  after  all,  not  created  by  our  analysis,  but  dis- 
covered by  It,  and  are  clear  and  helpful  In  enabling  ns  to 
understand  the  concrete  situation  before  us,  when  we  attempt 
to  put  it  together  for  ourselves.  Wherever  this  method-««r 
be  applied,  analysis  is  superior  to  intuition,  and  the  analytical 
habit  of  mind  is  the  one  which  should  be  cultivated. 


EXERCISES  147 

rOH  FURTHER  RRADIMO 
P.  H.  Bradley,  Prkteiplet  of  LogUs,  pp.  414-415. 

BXBRCIBBS 

Compare  tfte  working  of  the  Intultiye  method  with  the  method  of 
analytic  expansion  In  the  following  situation* :  (a)  In  aeeklnr  a 
lodging  In  a  strange  town,  (b)  In  deaUng  with  a  case  of  alckneia 
(c)  In  estimating  the  value  of  "popular"  music  as  opposed  to  the 
music  of  H«h,  Beethoren.  and  -ahms.  (d)  In  accepting  the  tenets 
of  a   particular   religion,      (e)  Investing  one's  savings  In   stocks. 

(f)  In  estimating  the  ethical  vuiue  of  charity. 


CHAPTER  XIV 


NOVELTY  IN  INFERENCE. 


The  Problem.— 2  +  2  =4.  2  +  3  =  5.  This  procedure  Is 
typical  of  all  Inference.  We  put  together  two  or  more  prem- 
ises and  the  resultant  conclusion  is  an  item  of  information 
derived  from  neither  premise  alone,  but  from  both  taken 
together.  Let  us  take  a  more  complex  example.  2X4 — %  = 
7%.  The  number  of  possible  premises — i.  e.,  the  number  of 
distinct  items  of  information  which  can  be  combined  to  yield 
a  single  conclusion — is  theoretically  unlimited.  Any  addition 
sum  is  an  inference  which  furnishes  us  with  information 
derived  from  all  its  premises,  and  expressing,  from  a  certain 
viewpoint,  the  whole  truth  concerning  those  premises,  how- 
ever numerous  they  may  be.  So  too  with  statistical  informa- 
tion. The  arithmetical  mean,  in  conjunction  with  the  probable 
error,  furnishes  us  with  a  kind  of  telescoped  information  as 
to  the  behavior  of  a  large  group,  however  many  its  members. 
A  simple  curve  can  tell  us  at  a  glance  how  students  at  Cornell 
or  Harvard  tend  to  be  marked  by  their  instructors.!  A  differ- 
ent, but  equally  simple,  curve  can  inform  us  of  the  rate  at 
which  practise  makes  perfect.^  Both  curves,  however,  though 
simple,  express  the  result  of  innumerable  distinct  premises, 
and  are,  in  fact,  valuable  in  direct  proportion  to  the  number 
of  cases  which  they  sum  up.  So  too  a  chemical  formula  or 
botanical  law  may  express  briefly  and  clearly  the  result  of 
years  of  patient  observation  and  experimentation;  a  poem  or 
picture  may  sum  up  the  experiences  of  a  lifetime;  and  a  phil- 
osophical speculation  may  express  the  soul  of  humanity. 

The  problem  before  us  in  the  present  chapter  is  to  ask 
how  far  such  information  is  novel.  That  it  is  attained  by 
methodical  analysis  of  the  premises,  we  have  already  seen. 
It  remains  to  ask  whether  what  we  obtain  by  summing  up. 


1  See  FInkelsteln.  The  Markinn  Kimtrm  in  Theory  and  Practixe.  101.1. 

2  For  Home  recent  work  In  this  field,  see  J.  Peterson,  Erpcrimentt  in 
BaUTi)»»ing ;  the  Higniflrance  of  Learning  Curvet,  ioar.  Bzper. 
P«ych.,  Vol.  II,  pp.  178-224. 


M8 


A.   - 


SENSORY  NOVELTY  149 

or  by  putting  together,  our  premises  is  something  which  we 
already  possessed,  something  which  was  ours  all  the  time 
or  whether  it  is  in  any  strict  sense  new.  As  Mill  expresses 
it,  can  we  "argue  from  the  known  to  the  unknown"?  That 
is  to  say,  can  any  logical  manipulation  of  what  we  know  by 
any  possibility  lead  us  beyond  what  we  know— extend  the 
bounds  of  knowledge,  and  raise  the  veil  which  yet  conceals 
the  unknown  from  our  eager  vision? 

Sensory  Novelty.— Let  us  consider  for  a  moment.     There 
are  two  sources  of  knowledge,  (1)  sense-perception,  and  (2) 
intelligence.      So    far    as    sensory    experience  is  concerned, 
there  can  be  no  question  that  the  information  with  which 
we  are  furnished  through  these  channels  is  essentially  novel 
Color,  sound,  taste,  touch,  smell— an  experience  deprived  of 
these  would  be  poor  indeed,  and  direct  experience  of  these 
qualities  is  furnished   us   by   the   senses   alone.     No   logical 
manipulation  of  sensory  data— however  Intelligent  that  manip- 
ulations—can give  us  a  new  sensation.     That  is  beyond  the 
possibility  of  logic.    That  veil,  at  any  rate,  cannot  be  raised 
by  the  intellectual  function  of  inference.    Are  we  to  conclude 
from  this  that  the  function  of  intelligent  Inference  is,  after 
all,  to  accept  data  derived  from  another  source,  and  to  proceed 
to  classify?     Are  we  to  believe  that  sense-perception  alone 
is  the  source  of  novelty  in  our  experience?    Are  we  to  accept 
the  view  that  intelligence  can  combine,  analyse,  and  shift  the 
positions  of  sensory  data  relatively  to  one  another,  but  that 
to  add   to  our  positive  knowledge   is  beyond  the  power  of 
intellect?    In  other  words,  is  the  desiderated  extension  of  the 
bounds  of  knowledge  purely  a  matter  of  sense-perception  and 
is  inference  restricted  to  the  organisation,  to  the  re-arrange- 
ment of  contents  which  cannot  be  altered,  and  above  all  can- 
not be  increased  by  any  logical  manipulation  whatever? 

For  instance,  I  do  not  know  whether  there  will  be  any 
mail  for  me  today.  Will  inference  help  me?  I  turn  over  the 
probabilities  in  my  mind.  I  do  what  I  can  with  the  knowl- 
edge which  is  at  my  command.  I  analyse  it,  turn  it  over  and 
over,  alter  its  arrangement  by  looking  at  it  from  different 
angles  of  approach.  But  do  what  I  will,  any  conclusion  to 
which  I  can  come  remains  only  probable.  "There  may  be 
a  letter  from  X  or  y."    The  only  way  in  which  my  lack  of 


150 


NOVPXTY  IN  INFERENCE 


!  '■ 


knowledge  can  be  converted  into  actual  knowledge,  is  here 
by  senge-perceptlon.  The  postman's  ring,  followed  by  actual 
receipt  of  the  letter,  is  In  such  cases  the  only  satisfactory 
evidence.  Shall  I  receive  a  certain  appointment?  Again  I 
make  use  of  all  the  knowledge  at  my  disposal.  I  turn  over 
and  over  what  I  know  about  myself  and  about  the  other  candi- 
dates. I  bring  to  bear  all  that  I  have  heard  of  the  disposition 
of  the  man  wltK  whom  rests  the  final  decision.  Still,  there 
is  a  gap.  I  do  not  know  enough  to  feel  certain.  The  only 
satisfactory  evidence  is,  here  again,  by  sense-perception— the 
receipt  of  an  official  notice  of  my  appointment.  Again— Is 
the  liquid  before  me  an  acid  or  an  alkali?  My  knowledge 
tells  me  that  if  it  is  the  one,  it  will  turn  blue  litmus  paper 
red,  and  if  it  is  the  other,  it  will  turn  red  litmus  paper  blue. 
But  I  do  not  know  which  of  these  ifs  will  be  realised.  My 
knowledge  does  not  reach  far  enough,  and  no  amount  of  infer- 
ence will  stretch  it  so  as  to  bridge  over  the  gap.  The  only 
reasonable  thing  to  do  is  to  dip  In  a  piece  of  blue  (or  red) 
litmus  paper,  and  see,  by  actual  sense-perception,  what  takes 
place.  Then,  and  then  only,  shall  I  know.  These  and  a  thou- 
sand similar  instances  serve  to  illustrate  the  value  of  observa- 
tions and  experimental  appeal  to  sensory  experience,  over 
arm-chair  theorising. 

Intellectual  Novelty— It  looks,  then,  as  though  observation, 
tbe  appeal  to  sense-perception,  is  essential  in  discovering 
information  which  is  new.  And  yet,  before  commg  to  a  final 
decision,  let  us  examine  a  different  group  of  cases.  I  have 
a  thousand  dollars.  I  wish  to  invest  profitably,  and  yet 
safely.  There  are  two  Government  loans,  both  redeemable  in 
three  years,  but  the  one  pays  5%  interest  and  sells  at  par, 
while  the  other  pays  4%  interest,  and  is  selling  at  92.  Both 
are  equally  safe.  The  only  question  is,  whi'  i  investment  is 
the  more  profitable?  I  do  not  know.  If  I  could  find  out  with 
certainty.  I  should  be  acquiring  information  of  the  utmost 
importance  to  me.  Would  it  also  be  newf  It  would  at  least 
be  welcome  news— novel  in  the  sense  that  I  do  not  know  It 
now.  If  I  could  find  out,  there  would  be  an  addition  to  what 
r  know.  It  might  even  turn  out  to  be  novel  in  the  sense  of 
unexpected.  I  may,  in  fact,  be  on  the  point  of  making  an 
unwise  investment.  Perhaps,  then,  we  can  safely  regard 
such  information  as  new.  And  yet,  no  one  doubt,  that  this 
information  can  be  acquired,  and  acquired  by  procesieB  of 


INTELLECTUAL  NOVELTY 


151 


Inference  familiar  to  any  mathematician.  And  further,  a 
study  of  the  analytical  method  examined  In  the  preceding 
chapter  should  reveal  the  fact  that  such  Inference  is  restricted 
to  the  re-arrangement  of  contents  which  themselves  remain 
unaltered.  It  looks,  then,  as  If  It  must  be  possible,  at  least 
In  some  cases,  by  logical  manipulation  of  given  contents,  to 
obtoln  knowledge  which  Is  reasonably  regarded  as  novel. 

Let  us  take  another  case.    I  wish  to  know  what  some  writer 
means  by  a  technical  expression  peculiar  to  him— e.  g.,  what 
Locke  understands  by  "simple  mode"  or  Plato  by  the  term 
"Idea."     I  have  In  each  case  a  vague  notion,  derived  from 
grasping  the  author's  meaning,  as  best  I  can,  as  I  read  through 
his  works.     But  my  notion  tends  to  change  with  each  new 
Instance  of  the  term  in  question,  and.  in  short,  the  evidence 
Is  so  confllcUng.  that  the  only  safe  conclusion  is,  that  I  do 
not  know  what  Is  intended.    I  cannot  put  it  together  and  make 
one  thing  out  of  it.    If  I  could  really  discover  what  the  author 
means,   I   should  acquire   Information   which   I   certainly  do 
not  possess  at  present.    I  should  add  to  my  knowledge,    The 
result  would  be  new.    It  might  also  be  novel,  in  the  sense  of 
unexpected— perhaps  even  as  contradictory  to  the  view  which. 
In  my  present  state  of  Ignorance,  seems  least  unreasonable! 
How  can  I  find  out?    Mere  sense-perception  will  not  tell  me. 
The  instances  are  far  too  numerous,  and  the  viewpoints  far 
too  complex,  for  that.    I  collect  all  the  instances— which  may 
be  regarded  as  given  contents,  not  to  be  altered  In  the  coarse 
of  the  investigation.    Then,  by  classifying  these  data  in  such 
a  way  that  all  which  bear  upon  this  point  or  upon  that  are  put 
together,  and  every  case  which  Is  irrelevant  to  the  point  at 
Issue  is  excluded,  I  find  that  I  can  gradually  settle  one  dis- 
puted point  after  another,  until  in  the  end  I  am  able  to  formu- 
late  a  hypothesis  which  Is  Just  to  all  the  facts,  and  in  short 
gives  me  the  Information  vhich  I  was  seeking.    I  have  thua 
discovered  something  new,  and  have  discovered  It  by  proc- 
esses of  inferenc-    Arhlch  were  confined  to  re-arrangement  of 
contents  which  remained  unaltered  throughout.4 

Let  us  take  yet  a  third  case.  I  am  playing  a  game  of  chess, 
and  am  reasonably  familiar  with  the  moves  and  conventional 
gambits.  At  one  stage  of  the  game,  no  amount  of  inference 
could  tell  me,  or  anyone  else,  who  is  going  to  win.    We  must 


152 


NOVKLTY IN  INFKRENCE 


flght  it  out  and  see.  But  at  a  later  Btege,  my  opponent  iud- 
denly  says,  "Mate  In  four  moves."  I  know  enough  about  the 
game  to  see  that  I  am  seriously  endangered,  but  I  can  not 
see  that  I  must  necessarily  lose,  whatever  I  do.  I  move.  One, 
counts  my  opponent,  as  he  also  :.  )ves.  I  move  again.  Two, 
he  counts.  I  look  again.  Yes,  now  I  also  can  see  that  a  check- 
mate in  two  more  moves  is  inevitable.  From  my  knowledge 
of  the  moves  and  from  the  position  of  the  pieces  on  the  board, 
I  see  that  there  are  only  a  few  moves  which  are  possible  for 
me,  and  that  which  ever  of  these  I  take,  I  must  assuredly 
fall  a  victim  in  two  more  moves,  provided  that  my  opponent 
continues  his  attack.  In  this  case  my  inference  gives  me 
knowledge. 

So  far,  then,  we  have  seen  that  Information  which  la  new 
can  be  derived  in  two  ways.  There  are  aome  cases  in  which 
sense-perception  alone  can  suiBce,  and  no  amount  of  theorla- 
ing,  or  re-organising  what  little  knowledge  we  have,  can 
be  substituted  for  It.  There  are  other  cases  In  which  sensory 
experience  alone  seems  to  be  useless,  and  where  the  re-arrang- 
ing of  what  we  know  leads  to  information  which  Is  both 
important  and  new.  it  should  be  clear  from  an  earlier  chap- 
ters that  both  sensory  and  intellectual  elements  enter  Into 
the  acquisition  of  any  and  every  sort  of  knowledge.  So  that 
the  question  which  now  faces  us  Is:  How  Is  It,  that  in  some 
cases  inference  helps  us  to  knowledge,  while  in  others  no 
amount  of  "theorising"  leads  anywhere? 

The  Field  of  Relations.— To  this  question  there  are  two 
answers.  In  the  first  place,  admit  that  sense-perception  alone 
is  the  source  of  certain  kinds  of  knowledge — viz.,  knowledge 
of  sense-qualities  such  as  red,  warm,  hard,  painful,  etc., — still, 
there  are  other  kinds  of  knowledge  of  which  intellectual  per- 
ception alone  seems  to  be  the  source.  A  knowledge  of  straight 
lines  and  of  circles — i.  e.,  demonstrative  knowledge  based 
upon  figures  which  are  ideally  perfect — seems  to  go  beyond 
what  sense-perception  gives  us.  These  geometrical  figures  are 
constructed  in  conformity  with  intellectual  demands,  rather 
than  somehow  taken  from  sensory  experience;  for  in  fact, 
It  Is  very  doubtful  if  ideally  straight  lines,  for  instance,  have 
ever  been  met  with  in  sensory  experience.  So  too  arithmetic, 
the  knowledge  based  upon  the  relations  of  the  elements  of 


B  Chapter  X. 


THE  FIELD  OF  RELATIONS 


1S3 


the  number-series  1.  2,  3.  .  .  .  Beems  to  tra-ntcend  what 
we  meet  with  in  MOM-experience.  These  uoits,  each  one  ot 
which  is.  from  the  viewpoint  of  quantity,  ideally  equal  to 
every  other,  which  extend  in  a  progressive  series  from  zero 
to  infinity,  In  the  plus  or  minu"  Jirectlon— are  also  intellectual 
constructions  in  accord  with  intellectual  demands.  Here  also 
sense-perception  plays  a  role  which  is  at  least  subordinate. 
So  too  with  the  o,  b,  c,  the  x2  and  ift  of  algebra,  with  the 
cotine  alpha  and  tan  theta  of  trigonometry — in  a  word,  with 
mathematical  relations  generally.  These  all  furnish  ue  with 
information  which  is  of  great  importance  for  life  and  for 
science,  and  which  is  also  undoubtedly  new.  And — what  is, 
perhaps,  surprising — the  mathematical  sciences  demand,  and 
receive,  very  little  aid  from  sensory  experience.  The  knowl- 
edge of  mathematical  relations,  then,  seems  to  arise  leb  from 
sense-perception  than  from  intellectual  construction  and  intel- 
lectual perception. 

So  also  with  other  branches  of  Icnowledge.  "Conclusions 
drawn  from  premises  which  are  true,  are  themselves  true," 
"Entities  relattid  to  the  same  entity  are  related  to  one  another," 
"Every  event  has  a  cause,"  "If  things-in-themselves  are 
unknowable,  then  it  is  impossible  to  know  that  they  are 
unknowable,"  etcfi  To  put  it  shortly,  knowledge  of  relations 
appears  to  arise  from  intellect  rather  than  from  sense,  whether 
such  relations  are  mathematical,  physical,  logical,  or  what 
not.  Knowledge  of  qualities  is  furnished  us  by  sense-percep- 
tion; knowledge  of  relations  by  intellectual  perception. 

While  knowledge  of  relations  is  thus  not  derived  from 
sense-perception,  it  must  not  be  supposed  that  it  has  no  appli- 
cation to  the  sensory  field.  A  man  who  was  born  blind,  but 
has  studied  physical  and  psychological  optics,  including,  for 
instance,  the  theory  of  color-vision,  can  draw  inferences  which 
are  perfectly  correct  within  the  field  of  color-vision,  although 
as  a  matter  of  direct,  personal  experience,  the  blind  man  can 
never  verify  his  own  deductions  by  the  appeal  to  sensation. 
His  thought  is.  of  course,  moving  in  the  realm  of  laws.  i.  e., 
of  intellectually  apprehended  relations,  and  the  accuracy  with 
which  this  can  be  done,  even  in  the  complete  absence  of  the 
corresponding  sensory  experiences,  can  be  recognised   when 


•  For  further  inatances,  and  a  dlMuwion  of  sach  "tpri<Mi  knowl- 
edge," Ct.  Bertrand  Rujaell,  Problemt  of  Philotophi/,  e&p.  chsptcrs 
▼tr-viU. 


IM 


NOVELTY  IN  INFERENCE 


w«  itudy  the  writings,  e.  g.,  of  Helen  Keller,  which  Abound  In 
senie-imagery,  although  thli  can  have  only  a  symbolic  signifi- 
cance for  her.  So  also  a  comparative  psychologist  can  write 
intelligibly  about  peculiar  sense-experiences  of  certain  ani- 
mals, where  their  sense-organs  are  very  different  from  oura, 
and  their  sensations  can  be  apprehended  only  symbolically 
by  us.  So  too  many  short-sighted  persons  make  up  for  their 
sensory  deflclepcles  by  using  their  powers  of  Inference  to  a 
greater  degree,  and  to  some  extent  can,  as  they  say.  see  with 
their  intelligence  rather  than  with  their  eyes.  All  knowledge 
of  this  type  is,  however,  really  given  us  by  inference  from  lawa 
and  relations,  and  not  by  direct  sensory  experience. 

Latent  Knowledge.— The  second  answer  to  our  question  ii 
alao  concerned  with  relations,  but  is  not  so  indifferent  to  the 
presence  of  sensory  experience.  Let  us  consider  a  few  cases. 
If  I  know  that  add  turns  blue  litmus  paper  red.  I  can  apply 
my  knowledge  In  a  particular  case,  and  thus  discover  whether 
the  liquid  before  me  Is  or  is  not  acid.  The  appeal  is  here 
to  sense-perception — but  to  a  sense-perception  organised  so  as 
to  supply  an  answer  to  an  intellectually  prepared  question. 
I  arrange  or  organise  my  data  In  a  particular  way.  This  is 
a  matter  of  intellectual  construction.  I  then  observe  the 
result  which  follows  upon  my  construction.  I  have  not  added 
anything  to  the  data,  the  contents  before  me.  but  have  merely 
altered  thsir  order  or  arrangement,  i.  e.,  their  relations  to 
one  'another.  By  Interfering  with  their  relations  to  one 
another,  e.  g.,  by  dipping  the  litmus  paper  in  the  liquid,  I 
set  them  working  upon  one  another  in  such  a  way  that  they 
themselves  produce  a  result  which  I  observe. 

I^t  us  take  another  Instance.  I  wish  to  discover  the  mental 
age  of  a  child  suspected  of  being  backward.  I  apply  the  BInet 
tests  up  to  six  years,  seven  years,  eight  years.  In  the  tests 
for  the  eighth  year,  the  child  breaks  down.  He  Is  also  unable 
to  perform  the  tests  for  the  ninth  and  tenth  years.  I  conclude, 
on  this  evidence,  that  he  has  a  mental  age  of  seven  years. 
The  security  of  this  conclusion  depends  partly  upon  the 
experiences  which  have  been  summed  up  In  the  Blnet  scale, 
partly  on  the  carefulness  with  which  I  have  examined  the 
child.  The  summing  up  of  expprlen<««Mi  which  has  determined 
the  order  and  interrelation  of  the  tests  has  been  a  matter  of 
Intellectual  construction  rather  than  of  sensory  perception. 
The  behavior  of  the  little  child  resembles  the  behavior  of  the 


LATENT  KNOWLEDGE 


155 


Utmtis  paptT  in  the  acid  tent— it  Is  something  which  is 
o\mer\p(i,  and  then  Interpreted  In  the  light  of  the  law. 

In  HU(-h  caaea  1  dlB<  over  information  which  la  new,  but 
is  not  cnnflned  to  tli«>  realm  of  relationa.  I  discover  it  by 
manipuluilng  data,  by  chunging  their  relation  to  one  another, 
including  somi:  and  txcluding  othera,  introducing  a  certain 
order,  upproaching  nature  in  the  altitude,  not  of  a  mere  pupil, 
but  of  a  judge,  who  determines  what  queationa  shall  be  asked 
and  compels  the  witneMHcs  to  reply  to  those  questions.  Do  I, 
however,  al  itva  get  an  tuawer — t.  c,  does  this  method  always 
fur«iH&  tne  with  information?  We  must  admit  that  It  is  not 
unifoiml.v  AucctrSHful  .luat  aa  no  judge  can  legitimately 
extract  ftom  a  wlttu  <«s  mure  than  that  witness  Icnows,  so  no 
si'ientlilc  method  of  manipulating  data  can  extract  from  those 
data  more  than  is  there  to  be  extracted.  The  evidence  must 
in  some  sense  be  thtre,  awaiting  only  the  proper  method  for 
itH  discovery. 

Arguing  to  the  Unknown? — So  far  we  have  seen  that  novelty 
in  the  case  of  inference  Ih  either  a  matter  of  restriction  to  a 
particular  field — the  field  of  relations — or,  if  inference  leads 
to  discoveries  within  the  field  of  sense-experience  alao,  this  Is 
brought  about  by  some  re-urganisation  of  oui  experience  which 
readers  explicit  seasory  elements  which  were  somehow  there, 
but  In  a  latent  form — <.  e.,  auch  re-organisation  clears  the  way 
for  observation  We  should,  perhaps,  note  that  In  the  case 
of  relations  also,  these  come  to  be  apprehended  as  a  result 
of  some  reconstruction  of  our  experience.  Such  reconstruc- 
tion, then,  la  present  in  both  cases.  The  only  difference 
between  the  two  cases  is,  that  in  deallni;  with  relations  we 
are  dealing  with  form"-elemeets  of  our  experience,  while  in 
sense-perception  wf  have  to  do  with  "contenf'-elements. 
Neither  form  nor  content  Is  found  alone,  but  the  fom  Is 
always  the  form  of  the  content,  and  the  content  is  always 
found  in  a  par<^icular  form.  Thus,  in  reasoning  with  reference 
to  a  triangle  dr^iwn  on  the  board,  a  mathematician  deals  only 
with  the  "triangularity"  features  of  the  figure,  with  the 
geometrical  relations  of  line.^  and  angles  ideally  considered. 
But  In  addition  to  the  triangular  form,  there  is  always  a 
sensory  content  alao — c.  g.,  the  chalkiness  of  the  lines,  thAir 
position  on  this  particular  black-board,  the  time  of  day.  etc. 
The  mathematician  restricts  himself  to  the  field  of  mathe- 
matical relations,  and  neglects  the  sensory  features  as  sueb. 


156 


NOVELTY  IN  INFERENCE 


But  in  many  caees  in  geometry,  simple  sensory  inspection 
and  direct  sensory  cuniparison  of  unanalysed  figures  will  sug- 
gest to  us  the  idea  tliat  two  given  triangles  are  probably 
equal,  even  when  we  are  deflcien;.  in  respect  of  that  insight 
into  relations  on  which  the  mathematical  proof  properly 
depends.  It  is,  then,  in  the  apprehension  of  elements  hitherto 
unapprehended,  whether  such  elements  are  of  relational  or 
sensory  nature,  that  inference,  so  far  as  we  can  at  present 
see,  consists,  and  we  are  now  in  a  position  to  answer  our 
main  question  in  this  chapter,  viz.  How  far  our  conclusion 
gives  us  inforriaiion  which  is  strictly  new,  or — as  It  is 
expressed  by  Mill — whether  we  can  argue  from  the  Itnown  to 
the  unknown. 

We  have,  perhaps,  by  this  time  a  suspicion  that  knowledge' 
attained  by  car"ful  Inference  must  in  some  sense  have  been 
there  all  along,  awaiting  the  proper  construction  to  become 
visible  to  us.  And  in  the  case  of  discoveries  within  the  field 
of  sensory  experience,  we  have  already  seen  that  this  must 
be  the  case.  V\'e  cannot  construct  a  new  sensation,  but  can 
only  clear  away  obstacles,  or  take  a  new  viewpoint,  and  thus 
come  to  discover  what  was  there  to  be  discovered.  The 
case  of  relation»,  however,  has  not  been  adequately  considered. 
Can  we,  in  such  cases,  argue  to  the  "unknown"?  Let  us  con- 
sider a  typical  instance.  Suppose  I  discover  that  it  is  possible 
to  construct,  on  any  side  of  any  triangle,  a  parallelogram  equal 
in  area  to  parallelograms  of  any  size  whatever  constructed 
upon  the  other  two  sides  of  the  triangle.  This  was  something 
which  I  used  not  to  know,  something  which  I  should,  perhaps 
have  thought  difficult,  if  not  impossible,  before  I  went  through 
the  |i  of.'  In  going  through  the  proof,  then,  which  leads  to 
a  result  so  remarkable  and  unexpected,  do  I  at  any  place  argue 
from  the  known  to  the  unknown?    Let  us  see. 

Let  ABC  be  any  triangle,  and  let  BDEA  be  any  parallelo- 
gram on  the  side  AB,  and  AFGC  any  parallelogram  on  the 
side  AC.  It  is  required  to  construct  upon  the  third  side  BC 
a  parallelogram  equal  in  area  to  the  sum  of  the  parallelograms 
BE,  FC. 

Construction. — Produce  DE  and  GF  to  meet  in  H.  Join  HA 
and  produr    It  tJ>  meet  BC  at  K.    Parallel  to  KH,  draw  BI  and 


TThls  "problem"  was  solved  by  I'orpliyry  (Ttth  Cent.  A.  I).)  For 
the  "proor"  whli;li  follows,  I  am  Indebted  to  the  late  I'rofessor  Took 
Wilson,  of  Oxford. 


LATENT  KNOWLEDGE 


us; 


CJ.  to  meet  DE  and  OF  in  I  and  J  respectively.  Join  IJ. 
Then  shall  BIJC  be  the  parallelogram  required. 

Proof.— (1)  To  prove  that  BJ  is  a  parallelogram.  Because 
BH  is  a  parallelogram,  BI=AH;  and  because  AJ  is  a  parallelo- 
gram, AH=CJ.  Therefore,  since  each  =  AH,  31  =CJ.  And 
they  are  by  construction  parallel.  Therefore,  (by  joining  IC 
or  BJ)  it  can  be  shown  that  the  opposite  aides  I  J,  EC  are 
equal,  and  that  the  opposite  angles  of  the  figure  BJ  are  equal. 
That  is  to  say,  t^ie  figure  BIJC  has  been  proved  to  be  a  paral- 
lelogram. 

( 2 )  To  prove  that  BJ  —  the  sum  of  the  parallelograms  BE. 
PC.  Because  BE,  BH  are  parallelograms  on  the  same  baae 
BA  and  between  the  same  parallels  BA,  DH,  therefore  they 
are  equal  in  area.  Similarly,  IK  and  BH  are  equal  in  area. 
Therefore,  since  each  =  BH,  BE  =  IK.     Similarly  it  can  be 


158 


NOVELTY  IN  INFERENCE 


shown  that  CF  =  JK,  for  each  =  CH.     Therefore  the  whole 
parallelogram  BJ  =  the  sum  of  the  parallelograms  BE,  FC. 

That  is  to  say,  upon  BC,  the  third  side  of  the  triangle  ABC, 
a  parallelogram  has  been  cx)nstructed  which  is  equal  in  area 
to  the  sum  of  the  parallelograms  on  the  other  two  sides. 

Q.  E.  F. 

In  the  above  figure  we  have  constructed  something  which 
we  did  not  previously  Itnow  could  be  constructed.  That  is 
to  say,  we  have  really  disoo\ered  something  which  was 
unltnown  by  us.  Have  we.  however,  at  any  point  in  the  pro- 
cedure, taken  the  "inductive  leap,"  and  gone  beyond  our  knowl- 
edge by  arguing  to  the  "unknown"?  Let  us  see.  Our  whole 
reasoning  is  bast  J  upon  the  known  truths  concerning  paral- 
lelograms, as  applied  to  the  figure  before  us.  The  construction 
which  gives  us  the  particular  figure  allows  us  to  apply  our 
knowledge  In  a  way  in  which  it  was,  perhaps,  never  applied 
before,  and  thjs  to  ubtain  an  insight  which  is  novel.  But 
our  procedure  could  not  strictly  be  described  as  arguing  to 
the  unknown,  as  reasoning  from  something  which  Wv  do  know 
10  something  which  we  do  not  know.  Our  argument  con- 
sists throughout  in  making  clear  to  ourselves  facts  which  are 
already  implicit  in  what  we  know,  facts  which  are  present 
in  our  knowledge,  but  remain  latent,  awaiting  the  appropriate 
construction  to  become  clear  to  us.  We  remain  on  terra  firma 
the  whole  time,  and  take  no  "inductive  leap"  to  the  unknown. 

Could  we  perhaps  say — to  shift  our  ground — that  arguing 
from  a  particulir  experiment  with  this  single  •'epresentative 
of  the  class  "triangle"  to  all  future  triangle-experiences,  or 
to  all  possible  triangle-experiences,  is  arguing  from  something 
which  we  now  know  (this  particular  case)  to  something  which 
we  do  not  know  (the  "possible"  cases,  which  we  have  not 
yet  experienced)?  Certainly  not.  The  argument  is  not  con- 
cerned with  the  "here"  and  "now,"  but  is  based  upon  insight 
into  the  nature  of  the  triangle  and  the  parallelogram  as  such. 
It  is  insight  into  the  non-temporal  realm  of  mathematical 
relations,  and  the  question  of  time,  whether  past,  present, 
or  future,  is  strictly  irrelevant.  If  I  really  grasp  the  proof. 
I  have,  in  grasciog  it,  apprehended  the  interrelations  of  such 
figures  for  any  triangle,  and  we  may  safely  conclude  that,  so 
far  as  insight  into  relations  is  concerned,  we  never  argue 
from  the  known  to  the  unknown,  but  always  make  explicit 
something  which  is  implicit,  i.  e.,  something  which  is  already 


(,.— lv«,-Vl 


Lrt-cU/' 


EXERCISES 


159 


contained  In  what  we  know,  and  la  merely  awaiting  the  proper 
method  of  construction  to  make  It  explicit  and  clear  to  us. 

Conclusion.— Reasoning  from  the  known  to  the  unknown, 
then,  is  lmpoB8il)le.  Our  Inference  can  never  take  a  leap  and^, 
somehow  transcend  its  data,  the  premises  with  which  it  starts.  ( 
This  must  be  abandoned  as  a  chimera,  as  an  attempt  to  get  \ 
something  out  of  nothing.  Inference  is  always  a  matter  of 
analysis,  of  disentangling  something  which  Is  In  some  sense 
present— present,  i.  e..  in  the  sense  of  awaiting  discovery, 
awaiting  the  application  of  some  method  which  will  disen- 
tangle It  and  Jiake  it  plain.  This  method  of  analysis,  the 
method  of  disentangling  in  question,  is  what  we  understand 
by  Inference,  and  the  so-called  "novelty"  of  inference  con- 
sists, not  In  somehow  adventuring  into  realms  unknown,  but 
in  so  analysing  and  re-organising  our  experience  as  to  let  us 
see  our  way  where,  without  such  aid,  we  were  at  a  loss. 
Analysis  has  been  already  considered.  The  other  feature  of 
inference,  the  construction  which  makes  discovery  possible, 
remains  to  be  investigated  In  the  succeeding  chapter, 

FOR  FURTHER  READING 

B.   Bo..aii(riot.   LogUj,   Vol.   II.   pp.  g-9.     F.   H.    Rradlcy.   PHnciplek 
of  Logic,  pp.  410-429. 


EXERCISES 

CoDBlder.  In  the  following  raws,  how  far  the  "discovery"  Ig  really 
novel :  (1)  Hy  looking  up  a  date  In  a  reliable  history  book,  i  dlacover 
the  date,  which  I  did  not  know  before.  (2)  By  mixing  approximately 
equal  amounts  of  blue  and  yellow  on  the  color- wheel,  i  discover  that 
they  make,  not  (!»»  I  expected)  green,  but  «ray.  (3)  By  practising 
canfully,  passage  by  passage.  I  find  i  can  gradually  learn  to  play 
LIssfs  "I.a  Campanella"— which  I  had  always  thought  Impossible  for 
me.  (4)  By  drawing  a  curve,  I  find  that  the  center  of  a  Isdder  wW-'h 
slides  down  the  side  of  a  house,  describes  the  arc  of  a  convex  circle 
—whereas  l  had  previously  supposed  It  would  have  been  a  concave 
curve.  (5)  By  eating  porridge,  I  discover  that  It  tastes  good— where- 
as from  Its  optical  appearance  I  bad  always  supposed  It  would  not 
taste  good.  (6)  By  the  use  of  a  little  trigonometry.  I  discover  how 
far  distant  a  certain  ship  la  from  the  ship  on  which  1  um. 


Ji 


9 


CHAPTER  XV 


THE  SYSTEMATIC  CONSTRICTIVENESS  OF  INFERENCE 


Examples. — Add  one  to  one.  It  makes  two.  Add  one  to  two. 
It  makes  thre.\  If  we  have  grasped  the  principle,  we  can 
now  add  any  number  to  any  other  number,  or  indeed  can 
multiply  any  number  by  any  other  number.  We  can  also 
easily  learn  to  subtract  and  divide,  with  any  numbers,  or 
indeed  with  any  quantities  a.  b,  c  .  .  .  n,  whatever.  The 
whole  of  arithmetic  and  algebra  can  be  constructed  from 
these  simple  operations. 

Takf  a  ruler  and  place  it  upon  a  sheet  of  paper.  With  a 
pencil  against  the  edge  of  the  ruler,  draw  a  line.  If  we  have 
grasped  the  principle,  we  have  learnt  to  draw  any  number  of 
straight  lines.  Take  a  pair  of  compasses  and  describe  an  arc 
of  a  circle.  If  we  understand  the  principle  of  the  instrument, 
we  can  describe  circles  of  any  radius.  Incidentally  we  under- 
stand that,  by  keeping  the  compasses  open  with  the  same 
radius,  we  can  mark  off  equal  portions  along  either  straight 
lines  or  circumferences  of  circles.  With  these  three  simple 
premises,  let  us  proceed  to  construct  something  difficult — 
e.  g.,  a  regular  polygon  such  as  a  pentagon. 

To  construct  u  regular  pentagon:  Draw  any  straight  line 
AB,  and  on  It  mark  off  Ave  equal  divisions,  AC,  CD,  DB,  KF. 
EG.  With  center  A  and  any  radius,  describe  an  arc  HIJ, 
cutting  AB  in  1  With  center  O  and  the  same  radius  (AI), 
describe  an  arc  HKJ.  meeting  HIJ  in  H  and  J.  Draw  a 
straight  line  joining  H  and  J.  and  cutting  AG  in  L.  The  line 
AG  is  thus  divided  into  two  equal  portions  AL,  LO,  and  we 
now  know  bow  to  bisect  any  straight  line.  With  center  L 
and  radius  LA  (or  LG).  descrllw  a  circle.  On  the  circumfer- 
ence of  this  circle,  with  compasses  open  to  the  extent  AC 
(or  CD,  DE,  etc.),  mark  off  equal  portions  AM.  MN,  NO,  OP. 
Join  in  straight  lines  AM,  MN.  NO.  OP.  PA.  The  resulting 
figure  is  the  regular  pentagon  required.  If  we  have  grasped 
the  principle  of  this  construction,  we  now  know  how  to  con- 
struct a  regular  heptagon,  nonagon,  or  n-sided  polygon,  and 

160 


INFERENTIAL  CONSTRUCTIVENESS 


161 


I 


indeed,  can  in  principle  construct  the  whole  of  plane  and  solid 
geometry,  and  even  the  meta-geometries. 

Let  us  leave  mathematics,  and  conaider  life.  Reflect  upon 
the  egoism  of  childhood,  and  Its  negation  by  the  altruism 
of  adolescence.  Note  how  both  alike  are  negated  by  the 
mature  man,  who,  by  living  through  both  and  finding  both 
unsatisfactory,  gradually  rises  to  a  level  of  ethical  develop- 
ment which  is  above  such  one-sided  interpretations  of  life. 
If  we  grasp  the  principle  of  this,  we  have  the  key  to  under- 
standing etbichl  evolution  generally,  in  the  individual  and 
In  the  race,  and  Indeed  are  able  to  interpret  much  of  life  and 
history  which  i^  otherwise  confusing.! 

Let  us  take  yet  another  case  of  inference.  What  can  we 
infer  from  the  following  passage? 

"The  man  ex  veritate  in  the  first  place  understands  (with  an 
understanding  vhich  is  at  the  same  time  a  living  in  the  ful- 
ness of  feeling)  that  the  goods  of  this  world  are  not  true 
goods,  and  would  not  be  unmixed  with  evil  even  if  we  could 
have  them  all.  Pleasure,  health,  power,  consideration,  even 
the  sweetest  affection  so  far  as  it  is  fixed  upon  a  creature  who 
will  one  day  vanish  like  ourselves — all  is  vanity.  Even  the 
inward  peace,  which  is  the  reward  of  conduct  praiseworthy 
from  a  human  standpoint,  is  Illusory  and  fundamentally  sad. 
A  life  spent  in  the  pursuit  of  such  experiences  would  not  be 
worth  living. 

"In  the  second  place  he  understands  (and  feels)  that  person- 
ality, his  own  as  well  as  that  of  others,  has  an  intrinsic  value. 
Our  doing,  our  suffering,  our  aspiring  after  something  better, 
must  be  Justified.  They  are  not  vain  appearances,  but  reality. 
Whether  they  take  place  or  do  not  take  place,  cannot  be  all 
one — cannot  be  indeterminate  and  inconclusive.  Our  sight  Is 
darkened,  our  desires  are  disordered  and  impure,  because 
all  (or  nearly  all)  of  us  miss  the  road.  But  the  true  road 
exists.  "2 

We  can.  by  processes  of  Inference,  construct  at  least  three 
diverse  theories  of  life.  (1)  From  the  first  paragraph,  by 
negating  the  negations  of  the  ex  vcrit<U€  man,  we  can  obtain 
a  positive  theoiv  which  asserts  that  the  goods  of  this  world 
are  the  only  true  goods,  and  that  a  life  spent  In  the  pursuit  of 
pleasure,  wealth,  power,  love,  and  a  good  conscience,  is  foada- 

'  :1ie  aboTe  principtp  romeii  fn>m  liogel. 

3  FVom  n.  Varliioo.  The  Ortmt  Pmhtems,  1014. 


i  I 


162 


CONSTRUCTIVENESS  OF  INFERENCE 


mentally  Joyoua  and  the  only  life  worth  living— in  short, 
the  theory  of  materialistic  optimism.  (2)  From  the  second 
paragraph,  by  proceeding  in  a  similar  way,  we  can  construct 
a  view  of  life  which  asserts  that  personality  is  valueless,  that 
the  pursuit  of  one  end  rather  than  another,  and  in  a  word, 
aspiration,  effort,  and  hope,  are  without  signifflcance.  For- 
ward or  bacli— it's  all  one.  Upward  or  down — it's  Just  the 
same.  Life  is  meaningless  illusion,  and  there  is  no  "true 
road."  This  vitw  we  might  call  materialistic  pessimism. 
We  can  further  (la)  by  negating  the  pessimistic  statements 
at  the  materialistic  level,  obtain  additional  statements  of  an 
optimistic  kind,  such  as  that  aspiration  and  effort,  so  far  as 
productive  of  pleasure,  power,  etc.,  are  not  illusory,  but  "real- 
ity," and  that  a  personality  developed  in  the  pursuit  of  such 
aims  has  a  very  genuine  value.  So  too  (2a),  by  negating  the 
optimistic  statements,  we  can  obtain  additions  to  our  con- 
struction of  the  pessimistic  view — such  as  that  pleasure, 
health,  love,  etc.,  are  thoroughly  transitory  and  illusory,  and 
that  a  life  spent  in  pursuing  such  aims — indeed  any  life — is 
not  worth  living. 

On  the  other  band,  (3),  by  negating  the  optimist  and  pessi- 
mist view  both,  from  a  standpoint  which  is  not  materialistic 
but  spiritual,  we  can  construct  a  positive  statement  of  the 
ex  veritate  view.  For  the  ex  veritate  man,  it  is  only  so  far 
as  lived  at  the  materialistic  level,  that  life  is  not  worth  while. 
But  if  our  eyes  are  fixed  upon  higher  aims,  if  we  live  our 
life  in  an  Ideeltstlc  spirit,  then  pleasure,  health,  iote,  con- 
science, etc.,  take  on  a  new  significance.  They  are  no  longer 
evanescent  and  transitory,  but — when  taken  up  into  the  higher 
life  of  the  spirit— become  representative  of  the  eternal 
values.  Personality  ceases  to  be  the  mere  organisation  of 
animal  desires  at  an  animal  level,  and  becomes  the  reflex 
of  Divinity,  and  in  the  service  of  the  true  values  comes  to 
realise  the  value  which  is  properly  its  own.  Such  a  life 
is  life  at  its  deepest  and  best,  and  is  fundamentally  Joyous, 
and  well  worth  the  living. 

The  Problem:  (A)  How  Does  inference  Construct?- The 
above  examples  are  typical  of  the  constructiveness  of  infer- 
ence. It  is  well  known  that  occasions  slight  in  themselves, 
sometimes  entail  a  vast  number  of  important  consequences; 
that  from  the  twinkle  of  a  man's  eye,  or  the  tone  of  his 
voice,   a   popular   novelist   can   deduce   "whole    volumes"   of 


REQUISITKS  FOR  CONSTRUCTION 


163 


information  about  hl9  character,  that  from  two  or  tbreo 
facta  a  historian  can  reconstruct  a  whole  epoch,  that  from 
two  or  three  bones  a  palaeontologist  can  reconstruct  the  whole 
animal.  This  power  which  we  have,  to  construct  the  whole 
from  its  part  by  means  of  inference,  seems  very  remarkable, 
and  in  order  to  understand  it  we  must  endeavor  to  answer 
these  two  questions:  (a)  How  does  inference  construct — 
what  are  the  principles,  laws,  conditions  of  such  construction? 
and   (b)     How  far  is  inferential  construction  valid? 

The  first  requisite  of  construction  is  to  have  the  materials 
in  such  form  tliat  they  can  be  put  together.  That  is  to  say, 
construction  pre-supposea  analysis.  The  material  must  have 
been  separated  out  into  elements  which  can  be  used  in  a  new 
construction.  For  geometrical  constructions  the  straight  line, 
and  some  form  of  conic  section,  such  as  the  circle,  are  indis- 
pensable pre-requlsites.  For  the  solution  of  many  a  problem 
in  physics  the  a,  h,  c,  x'i  and  V'  of  algebra  are  conditions 
without  which  nothing  could  be  accomplished.  For  psycho- 
analysis, prepared  and  standarised  association-experiments 
constitute  the  units.  For  the  diagnosis  of  mental  ability, 
standardised  intelligence-tests  furnish  the  material.  And 
spealiing  genernHy,  some  Itind  of  unit  or  element,  the  prod- 
uct of  a  preliminary  analysis,  is  the  very  first  requisite  for 
inferential  construction. 

Elements  alone,  however,  are  not  sufflcient.  From  straight 
lines  and  circles  we  might  construct  triangles,  squares,  penta- 
gons, polygons  regular  and  irregular,  etc.,  ad  infinitum.  Prom 
the  units  furnished  by  the  grammatical  analysis  of  a  lan- 
guage, we  might  construct  a  dissertation  in  prose  or  verse 
in  the  language  in  question,  or  we  might  construct  a  gram- 
mar of  the  language.  From  algebraii-  units,  we  might  build 
up  solutions  of  purely  theoretical  problems,  or  we  might 
solve  pra<-tical  questions  in  almost  any  of  the  applied 
sciences.  From  the  units  revealed  by  psycho-analysis,  we 
might  proceed  lo  cure  a  hysterical  person  by  reconstructing 
his  dissociated  personality,-^  or  we  might  use  the  material  as 
evidence  in  support  or  refutation  of  some  cherished  psycho- 
logical hypothesis.  From  elements  alone,  anything  or  nothing 
might  be  constructed. 

A  second  requisite  of  construction,  then,  is  the  presence 
of  some  aim  or  purpose,  some  ideal  to  be  realised.     If  we 

»  Cf.  Morton  Prince,  The  Ditaoclatlon  of  a  PertonaUt]/. 


IM 


COXSTRUCTIVENKSS  OF  INFERENCE 


seat  ouraelvea  Ht  the  organ,  and  allow  our  flngera  to  wander 
aimleiily  over  the  keys,  we  are  not  likely  to  strike  a  "grand 
amen,"  or  indeed  to  produce  anything  which  could  be  dignified 
by  the  name  of  music,  any  more  than  the  machine  described 
by  Gulliver  after  his  visit  to  Laputa  was  likely  to  create  lttera> 
ture  of  a  permanently  valuable  character.^  It  may  be  true 
that  our  aims  become  realised  by  a  process  of  trial  and  error 
which  is  largely  governed  by  chance,n  and  our  constructions 
so  far  resemble  the  Laputan  machine.  But  even  so,  the  pret- 
ence of  a  definite  aim  is  necessary,  at  least  in  order  that  we 
may  know  whether  our  trial  was  an  error  or  a  success.  If 
we  attend  courses  at  a  university  with  the  aim  of  taking  a 
degree,  wc  are  far  more  likely  to  attain  a  degree  than  if  our 
attendance  is  without  aim  or  definite  purpose.  If  we  endeavor 
to  solve  a  definite  problem  in  simultaneous  quadratics,  we  are 
far  more  likely  to  succeed  than  if  we  are  Just  amusing  our- 
selves with  putting  together  x-  and  y'^,  a  and  b,  etc.  A  second 
requisite,  then,  of  constructive  Inference,  is  the  presence  of  a 
definite  aim  or  purpose. 

Even  this  is  iiot  quite  sufllcient.  It  is  not  enough  to  have 
(1)  a  number  of  elements  and  (2)  an  aim  of  some  sort,  or 
even  of  the  same  sort  as  the  elements.  It  is  not  any  and 
every  one  who  can  put  together  the  disjecta  membra  and 
make  them  into  poetry.  For  that,  it  takes  a  poet,  one  who 
understands  the  spirit  of  poetry.  So  too,  in  order  to  build 
a  cathedral,  something  more  than  good  intentions  plus  the 
materials  is  essential,  namely,  a  knowledge  of  architecture  at 
least.  So  too,  in  order  to  play  Beethoven's  sonatas,  something 
more  is  necesBary  than  a  knowledge  of  the  position  of  the 
notes  on  the  instrument,  plu»  an  ambition  to  play  the  works 
of  the  Master.  Long  practise  and  the  gradual  building  up 
of  a  technique  is  essential,  as  is  also  an  understanding  of 
musical  problems  and  of  the  sonata-form.  So  too,  in  order  to 
re-<-onstruct  a  iiistoriral  epoch,  Romething  more  is  necessary 
than  the  des'rf  to  do  so,  plus  certain  archeological  and  literary 
remains — viz .  the  historian's  familiarity  with  the  principles 
of  historical  coustruction,  both  in  general,  and  in  connection 
with  that  special  period. 

What  is  thi-!  tertium  quid  which  seems  to  be  necessary? 
The  technique  of  the  poet  or  musician,  the  understanding 
of  the  architect  or  historian — what  have  these  in  common? 

♦  (rulllvcr'n  Travelg,    Voyufiv  to  Laputn,     haitter  v. 

sCf.  W.  U.  rilUbury,  Fundamrntah  o/   Pnyrhology,  pp.  501   9. 


Validity  of  construction 


165 


At  least  tliii:  familiarity  witii  the  means  of  connecting  up 
materials  and  ideal,  a  grasp  of  the  srhemata  and  principles  of 
construction  applicable  in  these  particular  fields,  an  under- 
standing  of  the  structure  of  poetical  or  historical  compost- 
tion,  an  apprehension  of  the  nature  of  the  system  In  question. 
A  botanist  and  a  poet  observe,  let  us  say,  the  same  aim — e.  q., 
a  field  of  popplet).  They  have,  let  us  say,  the  same  aim — e.  g., 
to  describe  the  nature  of  those  popples.  But  the  scientist 
describes  their  nature  with  reference  to  the  systematic  study 
of  plants.  For  him  they  are  "phanerogams"  with  certain  medic- 
inal properties.  For  the  poet,  on  the  other  hand,  they  are 
are  a  vehicle  for  expressing  his  deepest  emotions  and  aspira- 
tions. They  aro  symbolic  of  the  laughter  and  tears,  the  grief 
and  Joys  of  life.  The  third  requisite  of  construction,  then. 
Is  a  grasp  of  some  system— scientific,  artistic,  or  what  not— 
in  which  we  can  put  together  the  elements  which  wo  bars 
analysed  out,  and  can  build  them  nearer  to  the  heart's  desire, 
shape  them  into  some  semblance  of  our  ideal.  Given  an 
understanding  of  the  principles  of  systematic  construction  In 
our  particular  field,  plus  elements  appropriate  for  use  in 
such  construction,  plus  an  aim  which  Is  realisable  with  such 
elements  and  by  such  methods,  we  need  nothing  further.  We 
can  proceed  to  construct  our  inferences. 

(B)  Validity  of  inferential  Construction.— Not  every  system 
constructed  by  inference  in  all  we  could  wish.  All  inferential 
construction  is  hypothetical,  and  there  are  many  possible 
systems,  many  rival  hypotheses.  We  are  even  advised,  as  a 
point  In  scientific  method,  to  keep  In  view,  throughout  our 
research,  a  number  of  alternative  possible  explanations,  so  as 
to  avoid  narrowness.  But  valuable  as  is  the  "method  of  multi- 
ple working  hypotheses"  from  a  practical  viewpoint,  we  can- 
not suppose  that.  In  strict  theory,  all  the  hypotheses  sug- 
gested are  equally  true.  Some  of  them  are  mutually  exclu- 
sive— in  which  case,  one  at  least  must  be  false.  How  are  we 
to  choose  between  rival  hypotheses?  How  can  we  discover 
which  of  the  conceivable  systematic  constructions  Is  the  best7 

Do  plants  whose  leaves  are  particularly  sensitive  to  light 
have  an  organ  analogous  to  the  primitive  eyes  found  in  some 
parts  of  the  animal  system? — Or  must  we  seek  some  other 
hypothesis?  Is  the  three-color  hypothesis,  or  the  four-color 
theory  to  be  accepted  as  an  explanation  of  the  facts  of  human 
color-vision?    Is  Locke  a  critical  idealist,  or  Is  he  an  empirl- 


166 


CONSTRUCTIVKNF.SS  OF  INFERENCE 


cist  with  leanings  towards  realism?  Are  Plato's  "Ideas"  to  be 
regarded  as  Super-thlnga,  or  merely  as  M-lentlflc  methods?  In 
every  field  of  research  this  problem  is  pressing.  Is  there 
any  method  or  criterion  which  will  enable  ua  to  choose  with 
certainty  between  rival  explanatory  constructions? 

There  is  no  royal  road  to  such  knowledge,  no  short  cut 
across  the  devious,  triul-and-error  methods  of  experimental 
Inquiry.  Progrcbs  in  knowledge  can  alone  decide,  progress  in 
verifying  or  in  refuting  some  suggested  hypothesis  by  strict 
and  careful  reference  to  the  data.  What  hypothesis  Is  the 
best,  can,  in  the  end,  only  be  discovered,  not  by  some  system 
Introduced  ab  rxtra,  but  from  a  study  of  the  system  which  Is 
already  present  In  the  data,  at  least  in  germ.  But  to  find 
out  what  system  actually  is  present  in  the  data  is  often  a 
matter  of  prolonged  experimentation  with  results  which 
obstinately  remain  doubtful.  And  it  is  only  very  gradually 
and  tentatively  that  a  rival  hypothesis  can  be  eliminated,  and 
a  more  correct  one  established. 

What  is  the  system,  or  what  are  the  systems,  according 
to  which  animal  cells  multiply?  Could  we  think  thlp  out? 
We  might  imagine  that  the  cell  would  grow  by  taking  In  nutri- 
tion, until  the  tension  of  its  Increasing  bulk  became  too  strong 
for  the  containing  membranes,  and  it  broke,  aided  by  the 
pressure  of  external  forces — such  as  the  beating  of  waves  in 
the  case  of  wat^r-aniinals — into  two  or  more  cells,  each  small 
enough  to  maiiuain  itself  in  relative  equilibrium  over  against 
the  forces  of  the  environment.  Beyond  this,  perhaps,  one 
could  hardly  go  a  prion.  The  functions,  however,  of  nucleus 
and  nucleolus,  of  centrosome  and  chromosome,  and  in  a  word 
of  all  the  finer  and  more  intricate  elements  which  play  their 
part  in  the  division  of  cells,  could  never  have  been  discovered 
In  this  way.  Observation  and  patient  experimenting  alone 
could  have  discovered  the  system  which  is  the  »y$tem  of  the 
data. 

It  is  necessary,  then,  to  obtain  insight  into  the  appropriate 
system — the  particular  system  to  which  the  data,  in  some 
sense,  already  belong — If  we  wish  to  construct  a  system  which 
will  be  valid.  Given  a  curve  to  be  completed,  it  makes  a 
serious  difference  whether  we  try  to  complete  it  by  construct- 
ing the  form  of  a  circle,  of  an  ellipse,  or  of  a  parabola.  The 
evidence,  however,  which  is  to  guide  our  choice,  Is  to  be  dis- 
covered only  by  a  careful  analysis  of  the  data,  e.  g.,  of  the 


1/ 


CONCXUSION 


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curre  in  quMilon.  80  too  tb«  principlM  which  arc  to  gulda 
our  reconitruction  of  the  thought  of  PUto  or  of  Lock*,  mutt 
be  sought,  not  in  a  itudy.  e.  g.,  of  Neokantian  phlloiophy,  but 
in  a  careful  iti'.dy  of  Plato  himself,  or  of  Locke  himself.  In 
the  last  analy«!e,  it  Is  there,  if  anywhere,  that  the  Platonic 
system  or  the  Lockian  system  will  be  discovered.  Any  other 
studies,  however,  ingenious  and  however  erudite,  can  lead  only 
to  unverified  hypotheses. 

Conclusion. — Our  general  conclusion  Is  that  from  elements 
which  are  either  given,  or  discovered  by  analysts.  In  a  concrete 
situation.  Inference  constructs  a  system  which  either  puts 
together  the  elements  from  a  new  viewpoint,  or  carries  further 
a  system  which  Is  already  present  in  a  fragmentary  or  partial 
form  In  the  elements  themselves.  Choice  tietween  the  different  > 
possible  BystemR,  or  In  general  the  validity  of  inferential 
construction,  can  be  determined  only  by  strict  analysis  of 
the  concrete  situation,  leading  to  the  discovery  of  a  system 
which  is  already,  to  some  extent  at  least,  present  or  Implicit 
In  the  data,  and  then  using  this  system,  and  this  system  only, 
as  a  principle  of  construction. 


FOR  FURTHER  READING 


F.  II.  Ilradley,  Princtplft 


R.  Rowuiquet.  Logtc.  Vol.  II,  pp.  30-42. 
of  Looic,  pp.  41 2-414,   410-429. 

KXKHCIMEH 

1.  Construct  from  the  foUoirInK  paoMge  a  theory  of  rood  and 
evil.  When  yuu  have  rontitrueted  the  theory,  point  out  (1>  bow  yon 
have  proceeded,  and  (2)  how  far  your  re»ult  may  reaaonably  be 
regarded  aa  valid : 

"We  are  aaklng  whether  goods  and  evils  and  obligatlona  exist  In 
physical  facts  per  tc.  8un>ly  there  Is  no  tiatuii  for  good  and  evil  to 
exist  In,  in  a  purely  Insentient  world.  How  can  one  physical  fact, 
considered  simply  aa  a  phyHtraJ  fact,  be  'better'  than  another?  Bet- 
terness  Is  not  a  ^pOiyslcal  relation.  In  Its  mere  material  capacity,  a 
thing  can  no  more  be  good  or  bad  than  It  can  be  pleasant  or  painful. 
Oood  for  what?  Oood  for  the  production  of  another  physical  fact, 
do  you  aay?  Itut  what  in  a  purely  physical  universe  demands  the 
production  of  that  other  fact?  riiystcal  facts  simply  are  or  are  not; 
and  neither  when  present  or  absent,  can  they  be  suiHHised  to  make 
dcmandx.  If  they  do,  tUey  can  only  do  so  by  having  desires;  and 
then  they  liave  ceased  to  t>e  purely  physical  facts,  and  have  become 
facts  of  conscious  sensibility."     (James,  WUl  to  Brlirre,  etc.,  p.  190). 

2.  Construct  from  the  following  pamiaRe  a  theory  of  the  habituat 
work  of  thought.  Then  point  out  (1)  bow  you  have  proceeded,  and 
(2)  how  far  your  remilt  may  reasonably  be  regarded  as  valid  ; 

"Our  tnrtelUgence  can  place  Itself  within   the  mobile   reality,   and 


MICROCOPY    RESOLUTION   TEST   CHART 

(ANSI  and  ISO  TEST  CHART  No.  2) 


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2.8 


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S'.S  Rochester.    Ne«   York         14609       USA 

'-as;  (716)    482  -  0300  -  Phone 

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168 


CONSTRUCTIVENESS  OF  INFERENCE 


adopt  Its  cfasetesgly  changing  direction — can  grasp  It  by  means  of 
that  intellectual  sympathy  wbicb  we  cali  intuition.  This  la  difficuit. 
I^e  mind  has  to  do  Tiolenc>  "-.o  itself,  has  to  reverse  the  direction 
of  the  operation  by  which  ''.  habitually  thinks,  has  perpetually  to 
revise,  or  rather  to  recast,  all  its  categories.  But  in  this  way  it  will 
attain  to  fluid  concepts,  capable  of  following  reality  in  all  Its  sinuosi- 
ties and  of  adopting  the  very  movement  of  the  inward  life  of  things. 
To  philosophise  is  thus  to  Invert  the  habitual  direction  of  the  woric 
of  thought."  (Bergson,  Introduction  to  Metaphyaica,  trans.  Ilulme, 
pp.  69-70). 

3.  Construct  from  the  following  passage,  (1)  a  theory  of  the  way 
of  philosophy,  (2)  a  theory  of  the  way  of  life,  and  then  point  out 
(a)  the  nature  of  your  procedure  in  each  case,  (b)  the  reasons  for 
which  your  result  may  be  regarded  as  valid : 

"This  I  take  to  be  the  way  of  philosophy,  of  any  philosophy  which 
aeelcs  to  be  consistent.  It  is  not  the  way  of  life  or  of  common  knowl- 
edge, anrl  to  commit  oneself  to  such  a  principle  may  be  said  to  depend 
apoq  ctholce.  The  way  of  life  starts  from,  and  in  the  end  it  rests 
on,  dependence  upon  foellng,  upon  that  which  In  the  end  cannot  be 
stated  Intelligibly.  And  the  way  of  any  understanding  of  the  world 
short  of  philosophy  still  rests  on  this  basis.  Such  understanding 
may  despise  feeling,  and  may  claim  to  have  risen  into  a  higher  region, 
but  in  the  end  It  will  be  Inconsistent  and  be  found  to  stand  on  that 
wbich,  taken  as  truth,  does  not  satisfy.  Outside  of  philosophy  there 
is  no  consistent  course  but  to  accept  the  unintelligible,  and  to  use 
in  its  service  whatever  ideas  seem,  however  inconsistently,  to  work 
best.  The  man  who  stands  on  particular  feeling  must  remain  outside 
of  philosophy.  If  you  are  wlUlng  to  be  inconsistent,  you  can  never 
be  refuted,  and  that  Is  why  philosophy  can  be  said  to  depend  upon 
choice."     (Bradley,  Eaaaya  on  Truth  and  Reality,  p.  235). 


CHAPTER  XVI 


THEORY  OP  INFERENCE  (1) 


The  Problem. — So  far  we  have  seen  that  inference  has  the 
four  main  characteristics  of  dependence,  analytical  expansion, 
novelty,  and  systematic  constructiveness.  The  relation  of 
these  characteristics  to  one  another  appears  to  be  somewhat 
as  follows:  First  we  analyse  down  to  elements  which  exhibit 
a  certain  inter-dependence  or  law.  Then  we  proceed,  iu 
accordance  with  this  law  of  inter-dependence,  to  construct  a 
system  which  either  makes  explicit  the  inter-relation  of  the 
elements  discovered  by  the  analysis,  or  carries  further  and 
completes  the  system  of  which  these  elements  already  consti- 
tute a  fragment — as  a  given  curve  may  be  completed  in  the 
form  of  a  circle  or  parabola.  In  this  way,  whether,  by  carry- 
ing the  system  further,  we  construct  something  new,  or 
whether,  by  our  mere  analysis,  we  discover  elements  present 
but  hitherto  unnoticed,  inference  leads  to  discovery,  to  novelty, 
and  inference  may  accordingly  be  defined  as  the  discovery  of 
knowledge  by  constructing  a  system  based  upon  analysis  of 
a  given  concrete  situation. 

The  problem  of  the  present  and  succeeding  chapters  is  to 
construct  a  "theory"  of  inference  comparable  to  our  theory  of 
Judgment,  to  re-state  our  present  findings  in  terms  of  the 
sensory  and  intellectual  factors  in  our  thought,  and  in  short 
to  supply  an  answer  to  two  questions — (1)  the  question  of 
fact,  the  question  of  the  part  actually  played  in  inference  by 
sensory  and  intellectual  factors,  and  (2)  the  question  of 
validity,  the  question  of  the  reliability  and  satisfactoriness 
of  inference.  Tn  the  present  chapter  we  shall  deal  with  the 
first  of  these  questions. 

The  Sensory  Elements,  (A)  In  Dependence. — ^Let  us  first 
of  all  consider  the  more  empirical  instances.  "If  the  ground 
is  wet,  the  corn  will  rot."  "If  I  do  not  hurry,  I  shall  miss 
my  car."  Is  any  part  played  here  by  sensory,  as  opposed  to 
intellectual,  factors?  Let  us  see.  The  instances  appear  to 
be  analogous  to  what  we  called  "Judgments  of  experience"  in 


H 


169 


170 


THEORY  OF  INFERENCE 


an  earlier  chapter.     Such  cases  are  all  generalisations  from 
experience,  and  from  an  experience  which  has  been  largely 
sensory.    The  wetness  of  the  ground,  and  so  far  as  that  goes, 
the  earthiness,  the  ground-ness  of  the  ground,  are  matters  of 
sensory  experience.    So  too  with  the  appearance  of  the  corn. 
The  discoloration,  softness,  etc.,  produced  by  the  rot  are  all 
largely  matters  of  seeing  with  the  eye,  testing  with  the  touch 
of    the   finger,    etc.     The   question   of   causation   is   usually 
regarded  as  intellectual — we  do  not  see  what  it  is  that  causes 
the  rot,  but  infer  or  reason.    Still,  if  we  were  r'.ght  in  attri- 
buting a  certain  continuity  to  our  sensory  experience,  the 
gradual  cl  "^nge  from  the  firm  yellow  corn-seed  to  a  mushy 
discolored  lumy  of  pulp  might  be  regarded  as  sensory,  pro- 
vided that  we  abstract  from  all  attempts  to  account  for  or 
explain  the  changes  in  question.     That  Is  to  say,  the  mere 
apprehension  of  the  mushiness  at  each  stage  of  the  degenera- 
tion of  the  seed  can  be  regarded  as  a  matter  of  sense-experi- 
ence.    But,  it  may  be  asked,  does  sensory  apprehension  of 
this  kind  really  touch  the  question  of  "dependence"  at  all? 
Our  answer  must  be.  No,  or  at  any  rate  not  directly.    The 
dependence  of  rot  upon  damp  cannot  be  claimed  as  a  matter 
of  direct  sensory  experience.     The  nearest  we  can  come  to 
this  is  in  the  continuous  apprehension  of  degeneration  in  the 
damp  medium.    This  may  be  regarded  as  a  sensory  correlate 
of  causal  explanation,  but  in  general,  it  is  in  apprehending 
the  facts  to  be  explained,  in  taking  in  the  wetness  of  the 
soil  and  the  mushiness  of  the  seeds,  though  without  putting 
two  and  two  together  and  drawing  a  conclusion,  that  sensory 
apprehension  plays  a  part  here.    So  too  sensation  assures  me 
of  my  hurrying  or  not  hurrying,  of  the  car  standing  still  and 
of  my  reaching  it,  or  of  the  car  moving  and  of  my  remaining 
upon  the  spot.    But  the  connection  of  these  facts,  the  depend- 
ence of  my  reaching  the  car  upon  my  hurrying,  in  a  word, 
apprehension   of   the   relation    between   these   two   elements, 
seems  to  be  a  matter  of  intellectual,  rather  than  of  sensory 
experience.    Thus  we  see  that,  in  both  cases,  the  role  of  sensa- 
tion seems  to  be  to  furnish  us  with  a  concrete  situation,  with 
facts,  material,  or  data,  but  not  in  any  sense  with  explanation, 
with  apprehension  of  relations  of  dependence,  whether  logical 
or  causal.    The  "hypothetical"  element,  as  such,  is  non-sensory. 
There  is  no  "If    .     .     .     then"  about  sensation.     All  that 


SENSORY  ELEMENTS 


171 


sense-experience  can  do  in  sucli  cases,  then,  is  to  supply  us 
witli  the  materials  for  inference,  with  a  concrete  situation. 

What  are  we  to  say  about  the  less  empirical  cases,  e.  g., 
about  mathematical  dependencies?  The  equilaterality  of  a 
triangle  is  logically  connected  with  its  equiangularity,  so  that 
there  is  a  relation  of  Interdependence.  Does  sense-perception 
play  auy  part  here,  or  is  this,  perhaps,  a  case  of  "pure"  rea- 
soning, of  reasoning,  that  is  to  say,  unmixed  with  anything 
sensory?  So  too,  in  such  a  case  as  x2+y2  =  ^o,  if  we  already 
know  that  y  =  «,  we  know  with  mathematical  certainty  that 
X  —  2.  That  is  to  say,  the  conclusion  a;  =  2  is  dependent  upon 
the  two  premises.  Does  sense-perception  play  any  assignable 
part  here?  Or  are  we  to  accept  the  theory  that  mathematics 
is  the  creation  of  pure  thought?  There  is  no  doubt  that,  what- 
ever role  sense-perception  may  play  in  such  cases.  It  will  be, 
at  best,  a  very  subordinate  one.  In  the  case  of  geometry,  we 
may  point  to  the  fact  that,  while  all  our  geometrical  reason- 
ing is  general,  and  is  concerned  with  any  triangle  and  not 
with  this  particular  triangle,  still  we  do  not  seem  able  to 
proceed  without  a  figure  of  some  sort.  Such  a  figure  has 
definitely  sensuous  characteristics.  If  drawn  on  the  board,  it 
is  white  and  chalky;  if  drawn  on  paper,  it  is  black  and  Inky; 
if  drawn  in  the  Imagination,  it  is  vague  and  wavering  In  out- 
line. In  any  case,  as  apprehended  by  sense  or  in  sensuous 
imagination,  it  is  concrete,  connected  with  a  definite  back- 
ground, and  contains  a  thousand  other  characteristics  which 
are  equally  irrelevant  to  the  strictly  intellectual  grasp  of  the 
dependence  in  question.  So  too  in  the  case  of  algebra  or 
arithmetic,  the  x2  and  ys,  the  1,  2,  3,  etc.,  are  represented  on 
the  paper  or  in  the  sensuous  imagination  by  visible  symbols 
without  which  we  do  not  appear  able  to  proceed,  and  here 
also  sensation  supplies  our  thought  with  a  sensory  context 
which  is  largely  irrelevant  to  the  mathematical  law  In  ques- 
tion. From  a  consideration  of  such  cases  we  come  to  realise 
that,  while  inadequate  as  a  representative  of  mathematical 
laws,  sensation  does  play  a  part  in  steadying  the  attention,  in 
giving  the  intellect  a  point  d'appui  for  its  various  operations, 
in  short,  in  providing  us  with  a  concrete  situation. 

In  summary,  then,  we  can  state  that,  if  the  more  empirical 
cases  resemble  "judgments  of  experience,"  the  less  empirical 
cases  resemble  what  we  have  called  "symbolic  judgments," 
and  in  both  cases  we  see  that  sensation  plays  a  part  without 


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172 


THEORY  OF  INFERENCE 


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which  no  inference  would  be  possible.  For  it  supplies  us  with 
data,  with  a  concrete  situation  on  the  basis  of  which  we  can 
proceed  to  reason.  This  function  of  sensation  is  not  hypothet- 
ical, but  categorical.  All  explanation  or  hypothesis,  all  rising 
above  the  datum  to  a  grasp  of  principle,  of  a  law  of  depend- 
ence, belongs  to  factors  other  than  sensory.  But  the  situation 
above  which  we  rise  and  whose  law  we  come  to  grasp  is 
actually  present,  and  we  are  assured  of  it  by  sensation.  Of 
this  there  can  be  no  question.    It  is  categorical. 

(B)  In  Analytical  Expansion.— When  faced  with  a  given 
situation,  inference  does  not,  like  intuition,  regard  it  as  a 
totality,  as  something  to  be  accepted  or  rejected  in  toto,  but 
proceeds  to  take  It  apart,  to  break  it  up  into  smaller  factors, 
and  generally  to  reduce  it  to  its  constituent  elements,  so  that 
what  is  relevant  can  be  picked  out  from  what  is  irrelevant,  and 
elements  which  have  passed  unnoted  in  the  unanalysed  datum 
may  one  by  one  be  brought  under  the  mental  microscope  of  our 
attention,  and  nothing  may  escape.  In  this  process,  what  part, 
if  any,  is  taken  by  sense-experience?  That  it  furnishes  us  with 
the  situation  from  which  we  start,  we  have  already  seen. 
Does  It,  however,  do  more  than  this,  and  enter  in  some  way 
into  the  analytical  process  itself? 

In  a  way,  yes.  If,  during  the  process  of  analysing,  we  come 
upon  some  element  which  has  passed  unnoted  in  the  totality, 
we  apprehend  it  in  a  way  which  is  at  least  in  part  sensory! 
In  fact,  each  and  every  element  discovered  by  our  analysis, 
whether  previously  noted  or  not,  is  now,  at  any  rate,  appre- 
hended in  a  manner  which  we  can  consider  as  sensory.  Sensa- 
tion, then,  accompanies  every  step  of  our  analysis,  and  accom- 
panies it  pari  passu.  But  should  we,  on  this  account,  regard 
sensation  as  itself  exercising  the  function  of  analysis? 

Further  consideration  will  convince  us  that  the  presence  of 
sensory  apprehension,  in  the  final  as  well  as  in  the  earlier 
stages  of  analysis,  is  simply  the  presence  of  the  datum,  of  the 
concrete  situation  itself.  Analysis  cannot  go  beyond  its 
material,  but  must  remain  in  closest  contact  with  what  it  is 
analysing,  and  must  guide  its  every  step  forward  by  refer- 
ence to  what  has  been  given  to  It.  Hence  the  presence  of 
sensory  elements  at  each  step  of  the  analysis.  Sensation 
enters  into  our  analysing  in  no  sense  other  than  that  in 
which  the  given  situation  itself  enters  in— which  is,  as  a  guid- 
ing and  controlling  Infiuence,  at  once  the  material  and  the 


SENSORY  ELEMENTS 


173 

TtHfti"'  "'!'"  °\  ***'  P'"*^"'"'-  The  sensory  factor,  then.  Is 
strictly  not  analytical,  but  rather  Intuitive,  accepting  what 
18  given  as  a  wl.ole.  and  controlling  the  process  of  analysis  by 
providing  something  upon  which  factors  other  than  ^^nwry 
7c,TT  y  '"°<^tlons-a  complex  concrete  sltuaZ 
(C)  In  Novelty—Inference  Is  not  content  with  analysing 
a  ghren  situation.  It  stoops  to  analysis  In  order  to  make  dS 
coverles.   to   progress,   to   conquer   for  knowledge  something 

Tlf  J?:  '°  *^''  "'^'''  "  '•^^^'^^^^^  the  symbolic  judg 
ment.  which,  from  data  drawn  largely  from  actual  experlencJ 
makes  judgments  which  are  valid  beyond  the  field  of  13' 
experience  and  hold  good  for  possible  experience.    In  such 

thfn^'  nT'  'I  "''''''  *°'*'"'°'=^  ''^^'  *°  '^'  ^•«<=<'^"y  of  8om^ 
thing  new,  what  part.  If  any.  Is  played  by  sensation' 

There  are.  as  we  saw  above,  two  classes  of  cases:  (1) 
where  the  novelty,  the  new  Information  In  question.  Is  more 
cLfin  hT"^  ^''^'  *"'*  ^^^  ^^"'■^  *»»«  "^'^  'J'^covery  is  more 

decided  to  belong  more  properly  to  the  Intellect.  In  the  first 
case-|^  f,.  where,  by  dipping  red  and  blue  litmus  paper  Into 
a  liquid  and  by  seeing  the  blue  paper  turn  red.  we  InJ^r  that 

the  sensory  type.  As  such.  It  Is  strictly  analogous  to  the 
case  in  which  analysis  reveals  the  presence  of  sens^perceiv 
able  characteristics  hitherto  unnoticed,  and  the  novelty  Con- 
sists m  our  now  noticing  it.    That  Is  to  say.  the  function  of 

Crete  situation  In  its  full  concreteness.     The  inference,  how- 
ever, by  which  we  conclude  that  the  liquid  Is  therefore  an  acid 
goes  beyond  sense-perception  and  belongs  rather  to  the  field 
of  relatlons-m  this  case,  of  causal  relations 

In  the  second  case,  in  which  the  new  discovery  belongs 
more  especially  to  the  field  of  relations,  as  where  we  S 
discoveries  In  geometry,  or  where  a  person  born  blind  studied 
Physical  and  psychological  optics,  sensation  plays  a  very  su^ 
ordinate  role.  But  in  some  form  It  seems  always  to  b7pre^ 
ent.     The  figure  appears  to  be  necessary  in  geometrical  dlB- 

;Zm';/°V''/"°^  '°"°  •'^^^'-P'^*"  ^^-t  he  studies  l^ 
substituting  for  the  missing  visual  sensations  tactile  or  kin 
aesthetic  sensations,  so  far  as  this  is  poesihle-much  as  v,e 
try  to  understand  the  functioning  of  the  statocyst  in  Medusa 
or  Of  the  facetted  eye  in  Insects,  symbolically,  as  translated 


!i 


it 


i 


174 


thf:ory  of  inference 


into  sensory  terms  which  we  can  connect  up  with  our  actual 
experience. 

In  both  cases  the  function  of  the  sensory  element  appears  to 
be  to  steady  attention  by  concentrating  it  upon  a  particular 
lleld.i  This  special  field,  within  which  we  proceed  to  dis- 
cover relations,  is  the  concrete  situation  from  which  we  start. 
In  the  case  of  novelty,  then,  as  well  as  in  the  preceding 
cases,  while  the  novelty  as  such  is  discovered  by  factors  other 
than  sensory,  the  function  of  sensation  appears  to  be,  to  fur- 
nish us  with  the  concrete  situation  from  which  we  start,  and 
by  manipulating  which  we  somehow  advance  to  new  discov- 
eries. In  itself,  however,  sensation  is  not  progressive  or 
novelty-seeking,  but  accepts  passively  and  conservatively  the 
given  situation. 

(D)  In  Systematic  ConBtructiveness. — Discoveries  are  uiade 
either  by  our  reorganising  the  material  in  such  a  manner 
that  we  come  to  see  something  which  had  escaped  our  notice, 
whether  a  sensory  element  or  a  relation,  or  else  by  carrying 
further  some  system  which  is  already  present  in  the  data. 
Given  a  curve,  a  few  simple  geometrical  experiments  at  con- 
struction will  inform  us  whether  it  is  part  of  a  circle,  an 
ellipse,  or  a  parabola.  Given  an  examination  paper  written 
by  a  student  in  logic,  it  is  possible  to  form  a  fair  estimate  of 
that  student's  mental  ability  so  far  as  logic  and  kindred 
studies  are  concerned.  Given  a  few  experiments  upon  memory, 
we  can,  by  constructing  a  graph  from  our  data,  come  upon 
striking  and  suggestive  ideas  for  remembering  what  we  are 
studying.  In  such  cases,  what  part  is  played  by  factors  which 
could  be  called  sensory? 

There  appear  to  be  two  ways  in  which  such  factors  come 
into  play.  On  the  one  hand,  just  as  in  the  preceding  cases, 
sensation  furnishes  us  with  the  concrete  situation  from  which 
we  start.  The  given  curve,  the  examination  paper,  the  results 
of  the  memory  experiments — in  apprehending  all  of  these,  a 
part  is  played  by  sensation,  and  so  far,  the  function  of  sensory 
factors  resembles  precisely  their  function  In  the  cases  we 
have  considered.  But  on  the  other  hand,  it  seems  to  do  some- 
thing more.  Let  us  examine  an  instance.  Let  ABC  be  any 
given  curve.  We  proceed  to  test  it.  to  experiment  In  order  to 
see  If  it  is  a  ciriile.    We  draw  tw^o  chords,  AB,  BC,  and  bisect 


1  Cf.  O.  F.  Stout.  Analytic  Psychology,  1806.     Bk.  II,  cimpter  II. 


SENSORY  ELEMENTS 


175 


each  chord  at  right  angles.    The  two  bisecting  lines  meet  In 
D.     With  D  as  center,  and  with  a  radius  extending  from  D 
to  B  or  C.  we  describe  a  circle  BCE.     If  the  point  E  coin- 
cides  with   the   point   A.  so   that  the  curve  ABC   coincides 
with  a  portion  of  the  figure  BCE.  we  conclude  that  the  given 
curve    Is    an   arc   of   a   circle.     But   If    E    and    A    do    not 
coincide,  we  conclude  that  the  given  curve  must  constitute  a 
part  of  some  other  figure.    Either  It  la  a  portion  of  an  ellipse 
or  of  a  parabola,  or  perhaps  It  Is  altogether  Irregular.    We 
proceed  to  test  each  of  these  hypotheses  In  a  similar  way 
until  we  come  upon  one  which  seems  to  fulfil  all  the  con- 
ditions.    At  each  step  of  the  construction,  sense-perception 
Is  present.    We  see  the  chords  AB,  BC.    We  see  each  step  of 
the   construction  by  which  they  are  bisected.     We  «ee  the 
bisecting  lines  meet  In  D.    We  measure  out  the  radius  with 
the  aid  of  sense-perception.     We  see  the  curve  extended  so 
as  to  form  a  circle,  or  so  as  not  to  coincide  with  our  circle  as 
the  case  may  he.     At  every  point  of  our  construction. '  an 
appeal  to  sensory  factors  Is  Inevitable. 


I#tl 


\f\ 


In  the  process  of  analysis  considered  above,  we  noted 
that  sense-perception  accompanied  every  step  of  the  process. 
Are  the  cases  of  analysis  and  construction  perhaps  similar? 
In  the  case  of  analysis  we  saw  that  the  sense-perception  In 
question  was  In  fact  another  name  for  the  concrete  situation. 
Analysis  of  the  datum  revealed  elements  which  were  there 
but  had  not  been  noticed.  In  the  present  case,  however, 
there  Is  a  difference.    No  analysis  as  such  could  extend  or  pro- 


176 


THEORY  OF  INFERENCE 


[-i 


duce  a  curve,  and  while  In  some  sense  we  might  lay  that 
extension  or  legStlmate  production  of  a  curve  Is  "given"  along 
with  the  curve — for  we  do  not  create  our  extension  arbitrarily, 
but  construct  in  accordance  with  the  law  of  the  system  which 
is  given  along  with  the  given  portion  of  that  system,  viz., 
the  curve— still  the  extension  of  the  curve  is  not  in  any 
sense  present  for  sense-perception,  awaiting  only  the  direc- 
tion of  our  attention  to  it.  It  cannot  be  seen  before  we  have 
constructed  it.  For  sense-perception,  it  is  not  there.  The 
role  of  sense-purception  in  construction  is  thus  slightly  differ- 
ent from  what  v/e  found  it  to  be  in  the  case  of  analysis.  And 
yet,  in  spite  of  this  difference,  we  feel  that  in  both  cases  its 
function  is  to  apprehend  what  is  given,  and  not  to  add  or 
extend,  or  in  any  way  reconstruct  or  alter  the  given  situation. 
What,  then,  aie  we  to  say  its  role  i«?  Does  sensory  percep- 
tion recognise,  perhaps,  in  some  way  that  the  analysis  or  the 
construction  hhs  been  carried  through  correctly?  Is  it  a 
liind  of  verification  of  our  hypothetical  and  methodical  analy- 
sis or  synthesis?  Let  us  consider.  All  students  of  mathe- 
matics are  familiar  with  cases  in  which,  owing  to  some 
slight  error  in  drawing  the  figure,  perhaps  accidental  and 
unnoticed,  a  proof  will  end  with  the  conclusion  that  a  certain 
angle  is  both  equal  to,  and  greater  than,  a  right  angle,  or 
that  two  straight  lines  are  both  parallel  and  not  parallel, 
i.  e.,  are  parallel,  and  yet  meet  when  produced.  In  all  such 
cases  sensuous  perception  plays  precisely  the  same  role  as 
when  the  figure  Is  drawn  correctly.  By  its  aid  we  follow 
each  step  of  the  process,  and  notice  that,  e.  g.,  A  does  or 
does  not  coincide  with  E.  But  whether  it  does  or  does  not 
so  coincide,  is  not  usually  taken  to  be  a  matter  of  sensuous 
perception  as  such.  No  mathematician  would  dream  of  rest- 
ing any  portion  of  his  proof  upon  an  empirical  and  varying 
sensory  observation.  The  appeal  is  always,  not  to  sensation 
qua  sensation,  but  to  what  is  called  "mathematical  intuition," 
by  which  we  realise,  e.  g.,  that  two  straight  lines  as  such 
cannot  enclose  a  space,  that  two  plus  two  as  such  add  up  to 
four,  etc.  There  Is  no  as  such-ness  about  perception  so  far  as 
it  is  merely  sensuous.2    Verification,  then,  is  the  function  of 

2  Mathematics  Is  not  empirlml  In  the  same  sense  as  e.  g.,  my  belief 
that  the  sun  is  abining.  It  Is  not  «  m«tter  of  direct  aensory  pt.rr<»p- 
tlon.  The  difference  1«  the  difference  between  empirUche  and  reine 
Anacbauung,  or  between  the  conatatation  empirUjue  and  the  coiutata- 
tion  logique  of  a  logician  like  M.  Goblot.  (Ct.  B.  Goblot,  Trattf  Oe 
Logique,  1918,  sect.  40). 


INTELLECTUAL  FACTORS  -77 

factors  other  than  Benaory.  and  the  function  of  sensation 
appears  to  be  rather  as  an  accompaniment,  a  tine  qua  non,  of 
the  process  of  construction.  We  could  not  do  without  a  figure 
of  some  sort,  and  the  function  of  sensation  appears  to  be 
to  steady  the  i<ttention  and  concentrate  it  upon  the  features 
of  the  concrete  situation  which  are  to  be  utilised  in  guiding 
and  controlling  the  non-sensuous  process  of  systematic  con- 
struction. In  Uself,  however,  sensation  Is  not  constructive, 
but  simply  accepts  without  question  the  concrete  situation 
which  is  given  to  it,  whether  this  is  given  as  a  starting-point, 
or  as  a  result  of  construction. 

The  Intellectual  Factors:  (A)  in  Dependence.— "If  A.  then 
B;  If  not  A,  then  not  B;  if  B,  then  A;  and  if  not  fl.  then 
not  A."    The  cases  thus  symbolised  represent  what  the  Intel- 
lect   demands    as    the    four    phases    of    a    genuine    depend- 
ence.    Taken  together,  they  constitute  a  system,  a  mutually 
supporting  group  of  intellectual  demands  or  standards  with 
which   we  approach  the  empirical   data   in  our  attempts  at 
Inference,  at  obtaining  Insight  into  some  law.    As  such.  *.  e., 
as  constituting  a  systematic  group  or  organisation,  they  are 
subject  to  the  standards  which  govern  such  groupings,  that 
Is  to  say.  the  standards  of  identity,  difference,  and  organisa- 
tion,  Internal   and   external.     On    its    Intellectual   side,   our 
thought  directs  Its  attention  exclusively  to  those  features  of 
the  concrete  situation   which  are  relevant  to  this  point  of 
view,  and  the  result  of  the  application  of  such  standards  la 
always  to  leave  us  with  a  mere  skeleton  of  the  concrete  situa- 
tion with  which  we  started  out,  an  abstract  system  of  rela- 
tions which  satisfies  the  Intellectual  demand  so  far  as  it  con 
be   satisfied   without   going   illegitimately   beyond   the  given 
material.     The  details  of  this  have  been  already  sufficiently 
considered    In   our   study   of   the   appllcatlor   of   Intellectual 
standards  In  the  case,  for  Instance,  of  the  symbolic  Judgment. 
The  only  significant  difference  is  that  here,  Instead  of  stand- 
ards of  organisation  In  general,  and  of  consistency  within  a 
system  In  general,  we  have  a  very  definite  system  with  four 
main  aspects,  the  system  of  logical  dependence. 

(B)  In  Analytical  Expansion.— Analysis  Is  a  peculiarly 
Intellectual  function,  and  especially  Involves  the  standards 
of  Identity  and  difference.  The  concrete  situation  Is  envis- 
aged as  a  complex,  and  this  complex  is  taken  apart  and 
resolved  Into  Its  constituent  elements,  one  after  another.    For 


i 


\m 


178 


THEORY  OF  INFERENCE 


example.  I  have  applied  for  a  position,  and  am  usint  what 
powers  of  Inference  I  possess.  In  order  to  dlscorer  if  1  can. 
what  my  chances  are.    The  concrete  situation  from  which  1 
start  Is,  in  this  case,  all  the  information  of  whatever  kind  I 
have  which  In  any  way  bears  upon  the  subject.    It  is,  how- 
ever, not  clear  to  me.  but  Is  hopelessly  entangled  In  a  mass  of 
prejudices,  hopes,  and  fears,  which  effectually  interfere  with 
ay  Intellectual  vision.     By  making  use  of  the  standard  of 
dent  ty.  I  run  over  this  mass  of  material  with  a  single  idea 
In  mind,  and  s«.iect  every  element  which  In  any  way  bean 
upon,  c.  g.,  my  own  merits,  taking  these  one  by  one      By 
means  of  the  standard  of  difference,  I  reject  everything  which 
does  not  bear   upon  each   particular  point,  as  associations 
bring  up  fresh  material,  and  by  using  both  standards  in  this 
way  In  clearing  up  one  point  after  another,  I  at  last  have 
the  whole  of  the  Irrelevant  material  separated  off.  and  the 
whole  of  the  relevant  material  carefully  sorted  out.  so  that  T 
can  proceed  to  weigh  the  evidence  scientiflcally.  with  as  full 
knowledge  as  nosslble  and  without  undue  bias  from  emotion 
or  from  the  confusing  mass  of  the  material. 

Let  us  examine  another  case,  of  a  different  kind.    Take  the 
following  passage: 3 

"This  good.  then,  which  every  soul  pursues,  as  the  end  of 
all  Its  actions,  divining  Its  existence,  but  perplexed  and  unable 
to  apprehend  satisfactorily  its  nature,  or  to  enjoy  that  steady 
confidence  In  relation  to  it.  which  it  does  enjoy  in  relation  to 
other  things,  and  therefore  doomed  to  forfeit  any  advantage 
which  It  might  have  derived  from  those  same  things— are  we 
to  maintain  that,  on  a  subject  of  such  overwhelming  impor- 
tance,  the  blindness  we  hava  described  Is  a  desirable  feature  In 
the  character  of  those  best  members  of  the  state  Ja  whose 
hands  everything  is  to  be  placed?" 

This  passage  constitutes  a  single  sentence.  But  It  is  so  dif- 
ficult that  without  analytical  Inference  we  can  hardly  hope 
to  understand  It.  Let  us  analyse  it.  using  the  standards  of 
Identity  and  difference  so  as  to  take  one  thing  at  a  time 
Suppose  we  take  first  our  own  predicament— the  predicament 
In  which  "every  soul"  finds  itself. ,  We  are  pursuing  some 
good  as  the  goal  of  our  every  action.  We  intuit. /ely  believe 
In  the  existence  of  this  goal  towards  which  we  are  working. 

.•t.S^Sh«ft?""*"'  ^^  ""''  «*•  «W  B  to  506  A.     (Trans.  Davie- 


INTELLECTUA       '  \CTORS 


179 

but  are  unable  to  apprehend  its  nature.     We  are  perplexed 

know' What" the.r"'"''  'r'""'"*'  '""'^"  *"  '""'*»•  -^"--^  we 
Know  What  these  are  and  understand  their  nature    w<i  .m 

tt/'n'  Mn'  .'"'  *°^°r  ^  •^^-•'^  confldencrtTegl^d'S 
ourselves  to  be  worklng-not  exactly  knowing  what  It  Is   we 

Furth        "\  ^°""'*"^"^'  ""'^  ^°  "°*  »''>°-  w».ere  we     Und 
Further,  not  knowing   what  the  goal  of  life  Is    we  Hn  „«# 

know  how   we  should  arrange  our  life  In  reJ^cr  to  thl 

wisely,  and   therefore  cannot  make  the  most   of  them      I. 
Ignorance  of  the  goal  of  life,  from  which  It  derlj  .  Trwho  e 

uTi^Z  T:Z'  '"  "  "^"^^  -°  fundame„taTde1,«51e 
If  It    8  not  desirable  In  our  own  case,  is  it  not  still  leL 
BO  In  the  case  of  the  rulers  of  the  State?    if  our  great  m^ 

^ro'm  ^l\"':  "'"  "°^  '•*«  •'""^  ^  '^^'''-^  the  bUn^J?;    °*''° 

From  this  Instance  we  see  that  taking  a  single  view-noln* 

and  omitting  everything  which  is  Irrelevant  Introduc^'^^n 

^^iderable  clearness  Into  our  mental  grasp  of  what  wTthe", 

•"he^r/wr'^K-    '°  *'*  "^"^  ^-^^^  "^y  proceeding  to  mak; 

b^Jween  "dlv?nln?tr *  "\T  •°-«"«''"-.  <"•  the  dlstlncUon 
neiween    divining  the  existence  of  the  end  of  life  and  "anore. 
bending  the  nature  of"  other  things  such  aa  money   ple^e 
coui/      ;'";i'"'"  ''''""^  "I*  ""^  Po'°t  after  another    we' 

cear'er     inMnlT"'""  °'  *'^  ^^'»««  "  *  whole  mulh 
wf    ,  ,   ?  *       "''  ""*  '^^^  "^y  that  the  function  of  the  Intel- 
lectual  factors  In  analysis  is,  while  not  leaving  the  start^nJ 
point  or  m  any  way  going  beyond  the  information  which  S 
g^ven  to  us.  so  to  Introduce  the  standards  of  IdenZ  and 
difference,  as  to  lead  up  to  a  carefully  arranged  artlcuLnn- 
and  classlflcation  of  all  which  Is  relevant     ndrstriemo^" 
of  everything    vhlch  is  Irrelevant.    This  sifting  out  of  Tve7y 
e  ement  to  which  we  attend  leads  to  such  an  organiS 
of  our  thought  that,  in  place  of  confusion  and  mentercTa^ 
we  have  order  and  clearness.     It  may  be  at  times  that  tS 
grven  situation  ioes  not  contain  enough  informarto^tls?; 
our  every  question,  reorganise  It  as  we  may.    But  afJersuch 
analysis  has   been  completed,  we  at   least  know  where  we 

^e,f**,s*f„crde^^t.k\7JrthT?^uW.^'^^^^^^       '«7  "aly«Hi. 
discovered  tnat  the  good  Is  the  iSj  of  itfS.       P"^'*"«  analyslg  which 


if 


\  I: 


^  18C  THEORY  OF  INFERENCE 

stand.  No  Item  of  information  has  escaped  us,  and  If  an 
answer  is  there  to  be  discovered,  methodical  analysis  is  prac- 
tically certain  to  bring  it  to  light. 

(C)  In  Novelty.— Inference  is  not  fully  satisfied  with  the 
clearness  whicn  results  from  analysis.  It  is  not  merely  to 
make  our  thought  clear,  to  purge  it  of  confusion,  to  see  our 
way  more  plainly,  that  we  infer.  We  infer  so  as  to  discover 
an  answer  to  some  question  which  we  cannot  possibly  answer 
othtrwise,  to  make  our  way  out  of  some  difficulty  which  is 
otherwise  hopeless,  to  obtain  some  advantage  which  other- 
wise we  could  not  obtain.  Inference  discovers  something 
which  is  new.  In  such  discovery,  what  part  is  played  by 
factors  which  could  be  regarded  as  Intellectual? 

Let  us  consider.  In  the  above  passage  from  Plato,  for 
instance,  we  did  not  know,  until  after  our  analysis,  what 
was  meant  by  the  clause  "and  therefore  doomed  to  blindness 
.  .  .  "  Probably  we  did  not  feel  sure  about  what  was 
meant  by  the  -.indness"  of  the  statesmen.  Our  analysis 
thus  not  only  made  our  thought  clear,  but  made  us  see  our 
way  where  previously  we  had  been  entirely  in  the  dark.  In 
this  way  elements  concealed  by  their  context  can  be  discov- 
ered by  analyf '  -,  and  so  far  "novelty"  receives  the  came 
treatment  as  "analysis."  It  is  by  applying  the  standards 
of  identity  ana  difference  with  methodical  regularity  that 
we  make  discoveries  of  this  character,  that  we  light  upon 
something  which  was  already  there,  awaiting  the  application 
of  precisely  such  methods. 

There  are,  however,  other  cases  which  are  not  so  simple. 
For  instance,  most  problems  worked  out  by  simultar  'ous 
equations  give  us  information  which  is  new,  but  which  can 
hardly  be  said  to  have  been  present,  merely  overlaid  by  an 
irrelevant  and  confusing  context,  and  thus  concealed  from 
view.  I  miss  my  train,  and  two  hours  later  take  an  express 
which  follows  it  at  a  slightly  more  rapid  rate — e.  g.,  ten  miles 
an  hour  faster.  When  and  where  shall  I  catch  up  with  my 
proper  train  and  make  my  transfer?  There  is  no  doubt  that 
an  answer  to  this  question  in  some  sense  is  "given"  along 
with  the  conditions,  and  that  it  can,  as  we  say,  be  "worked 
out"  and  duly  discovered.  But  there  is  also  no  doubt  that 
something  more  is  needed  than  merely  taking  to  pieces  the 
dpta  and  scrutinising  them  one  by  one.  By  analybls  I  learn 
that  the  first  train  moves  at  forty  miles  an  hour;  that  my 


TT 


INTELLECTUAL  FACTORS 


181 


M.ii 


train  moves  at  flfty  miles  an  hour;  that  the  first  train  is  two 
hours  ahead;  etc.,  etc.  But  just  when  and  where  the  express 
will  catch  up  with  it— that  I  cannot  by  this  method  discover. 
It  has  to  be  worked  out.  In  such  cases  a  certain  extension 
of  the  intellectual  framework  of  the  concrete  situation  takes 
place,  and  it  is  in  relation  to  this  extension  that  the  answer  is 
worked  out  and  the  discovery  actually  made.  But  the  general 
method  does  not  differ  very  seriously.  I  use  x  and  y  in 
working  out  my  problem— i.  e.,  mental  counters,  sharply  differ- 
entiated Identities— and  it  is  by  the  substitution,  for  the  con- 
crete situation,  of  such  results  of  the  application  of  the 
standards  of  Identity  and  difference,  that  I  am  able  to  solve 
my  problem.  In  the  case  of  novelty,  then,  as  in  the  preced- 
ing cases,  the  function  of  intellect  Is  to  apply  the  standards 
of  Identity,  difference,  and  organisation  so  as  to  substitute  an 
intellectualised  model  which  Is  confined  to  essentials  for  the 
concrete  reality  which  contains  so  much  which  Is  irrelevant 
and  does  not  admit  of  that  intellectual  manipulation  which 
leads  to  discoveries. 

(D)  In  Systematic  Construetiveness. — Inferential  con- 
struction goes  beyond  mere  analysis,  but  still  without  chang- 
ing fundamentally  the  character  of  Its  data.  In  such  con- 
struction we  produce  a  straight  line,  for  Instance,  to  twice 
or  thrice  its  given  length.  It  is  still,  however,  a  straight 
line.  We  complete  a  curve,  e.  g.,  by  adding  the  missing  por- 
tions of  the  ellipse  of  which  it  constitutes  a  fragment.  The 
curve  is  still  the  same  curve.  On  the  third  side  of  a  given 
triangle  we  construct  a  parallelogram  equal  to  the  sum  of 
any  two  parallelograms  given  on  the  other  two  sides  We 
have  not.  however,  by  so  doing,  altered  the  nature  of  the 
given  triangle  or  the  given  parallelograms.  So  too  we  put 
together  all  we  know  of  the  character  of  Mr.  X,  and  Infer 
to  his  probable  course  of  action  in  a  certain  contingency. 
We  have  not,  however,  altered  the  nature  of  our  information 
by  so  extending  It. 

What  intellectual  factors  are  involved  in  such  construction? 
In  the  first  place,  we  use  the  standard  of  identity.  In 
extending  a  straight  line,  we  must  continue  to  produce  it  In 
one  and  the  same  direction.  In  completing  the  ellipse,  we 
must  hold  fast  to  the  method  of  constructing  the  ellipse  of 
which  the  given  curve  forms  a  part.  In  calculating  Mr.  X'a 
probable  action,  we  must  follow  the  identical  line  of  thought 


m 


182 


THEORY  OF  INFERENCE 


established  by  our  previous  knowledge.    In  the  second  place, 
we  use  the  standard  of  difference.    We  refuse  to  swerve  from 
the  identical  direction  of  the  given  line.    We  refuse  to  wander 
from  the  path  established  by  the  given  portion  of  the  ellipse. 
We   decline   to  allow  hopes  or    prejudices   to   influence  our 
calculation  of  Mr.  X's  probable  course  of  action.    In  the  third 
place,  we  make  use  of  the  standards  of  organisation,  Internal 
and  external,  in  constructing  our  system,  whether  that  system 
be  simple,  as  in  the  case  of  a  straight  line  or  ellipse,  or 
complex,  as  in  the  case  of  character-analysis  and  character- 
construction.     That   is   to   say,   in   constructing   systems   we 
employ  the  same  intellectual  factors  which  we  used  in  analysis, 
but  on  a  slightly  more  extended  scale— the  standards  of  iden- 
tity, difference,  and  organisation— and  employ  them  in  such 
a  way  that  we  start  with  a  concrete  situation  and  end  up  with 
a  mental  model,  an  abstract  plan  or  system  which  omits  many 
of  the  factors  present  in  the  given  situation,  and  now  Includes 
elements    which    go    beyond    the    situation    with    which    we 
started,  not  however  by  altering  its  character,  but  by  extend- 
ing ".  .     .  , 

Summary— The  Sensory  and  Intellectual  Factor*  in  Infer- 
ence.— In  inference,  then,  the  function  of  sensory  factors  is 
categorical,  intuitive,  conservative,  receptive.  Sense  receives 
without  question  what  is  given  to  it,  accepts  and  preserves 
it  without  alteration,  and  in  a  word  presents  us  with  the 
material  for  intellectual  operations,  a  concrete  situation  which 
forms  a  starting-point  for  inference.  The  function  of  intellect 
is  hypothetical,  analytical,  novelty-seeking,  constructive, 
progressive.  It  receives  nothing  without  question,  works  over 
what  is  given  to  it,  omits  here  and  extends  there,  re-arranges, 
sifts,  and  is  not  satisfied  until  it  has  substituted  for  the  given 
material  an  intellectualised  structure  from  the  inter-relation 
of  whose  parts  it  obtains  an  insight  which  is  new,  and  which 
leads  us  far  beyond  the  concrete  situation  which  was  orig- 
inally given  to  us.  In  so  doing,  however,  it  attempts  to  con- 
fine itself  to  alterations  and  additions  which  are  legitimate. 
How  this  is  possible,  we  must  now  proceed  to  inquire. 


FOR  FURTHER  RBADINO 

F.   H.    Bradley,   Principlca   of  Logic,   Bk.   Ill,   Part   I,   chapter   vll. 
J.    B.   Crelghton,    An   Introauctory   Logic,   chapter   xxlv.      J.    Royce, 


W.   Wimdt,   Logik,    (3rd 


EXERCISES  183 

Sources  of  Relioiout  Intight,  chapter  111. 
Edit).  Vol.  1,  pp.  296-301. 

EXERCISES 

1.  Construct,  In  systematic  form,  a  statement  of  the  part  played 
by  personality  In  the  world,  according  to  the  following  passage.  Then 
point  out  (1)  the  sensory  elements,  (2)  the  Intellectual  elements, 
used  In  your  procedure : 

"I  do  not  see  why  the  very  existence  of  an  Invisible  world  may 
not  lu  part  depend  on  the  personal  response  which  any  one  of  us 
may  make  to  the  religious  appeal.  I  do  not  know  what  the  sweat 
and  blood  and  tragedy  of  this  life  mean.  If  they  mean  anything  short 
of  this.  If  this  life  be  not  a  real  flght,  In  which  something  Is  eternally 
gained  for  the  universe  by  euccess.  It  Is  no  better  than  a  game  of 
private  theatricals  from  which  one  may  withdraw  at  will.  But  It 
feels  like  a  real  flghl,  as  If  there  were  something  really  wild  In  the 
universe  which  we,  with  all  our  Idealities  and  faithfulnesses,  are 
needed  to  redeem. — For  such  a  half-wild,  half  saved  universe,  our 
nature  Is  adapted."     (James,  Will  to  Believe,  etc.,  p.  61). 

2.  Conatruct  from  the  following  passage,  (a)  a  theory  of  Truth, 
(b)  a  theory  of  Reality.  Then  point  out  (1)  the  sensory,  (2)  the 
Intellectual  elements  used  in  your  procedure : 

"Reality  for  me  Is  one  Individual  experience.  It  Is  a  higher  reality 
above  our  Immediate  experience,  and  above  all  Ideality  and  relations. 
It  is  above  thought  and  will  and  aesthetic  perception.  But,  thooffh 
transcending  these  modes  of  experience,  it  Includes  them  all  fully. 
Such  a  wliole  U  Reality,  and,  as  against  this  whole,  truth  Is  merely 
Ideal.  It  la  Indeed  never  a  mere  Idea,  for  certainly  there  are  no 
mere  Ideas.  It  is  Reality  appearing  and  expressing  Itself  In  that 
onewrided  way  which  we  call  Ideal.  Hence  truth  Is  Identical  wit* 
Reality  In  the  sense  that,  In  order  to  perfect  Itself,  It  would  have 
to  become  Reality.  On  the  other  side,  truth,  while  It  Is  troth,  differs 
from  Reality,  and.  If  it  ceased  to  be  different,  would  cease  to  be  true. 
But  how  In  detail  all  this  is  possible,  cannot  be  understood.  (Bradley, 
Bstav*  on  Truth  OMd  Reality,  pp.  343-344). 


,  !' 


KlJ 


CHAPTER  XVII 


THEORY  OF  INFERENCE  (II) 
VALIDITY  OF  INFERE>':E 


The  Problem.— So  far  we  have  seen  what  part  is,  in  fact, 
played  in  inference  by  factors  which  are  Intellectual.  Sense 
supplies  us  with  the  concrete  situation  from  which  we  start, 
while  intellect  operates  by  taking  apart  this  situation  and 
presenting  us,  in  its  place,  with  a  mental  model  which  contains 
only  factors  which  we  can  understand— a  working  model 
which  we  can  take  to  pieces  and  put  together  again  because 
we  apprehend  its  principle  of  construction.  Our  present  prob- 
lem is  to  consider  how  far  this  procedure  is  valid,  how  far 
inference  is  reliable,  how  far  a  mental  model  which  we  can 
take  to  pieces  and  put  together  again  represents  accurately 
and  truthfully  the  reality  with  which  we  wish  to  make  con- 
tact, or  to  keep  in  contact. 

In  view  of  our  earlier  discussion,^  it  is  unnecessary  to 
inquire  now  in  what  sensory  validity  and  intellectual  validity 
respectively  consist.  In  such  cases  as  we  have  in  mind, 
validity  is  purely  a  matter  of  direct  sensory  apprehension, 
or  of  direct  intellectual  apprehension  of  the  results  of  apply- 
ing strict  intellectual  standards.  If  we  avoid  misleading 
associations,  and  subject  the  sensory  elements  to  direct  appre- 
hension, this  is,  as  we  have  seen,  ultimate,  the  last  court  of 
appeal,  and  is  so  far  satisfactory.  If,  again,  we  have  con- 
structed our  mental  model  after  strict  analysis  into  intellectu- 
alised  elements— sharply  differentiated  identities  which  can 
be  used  as  mental  counters — and  have  constructed  it  in 
accordance  with  the  principles  of  identity,  difference,  and 
organisation,  then  on  the  intellectual  side  it  is  so  far  satis- 
factory. The  only  question  which  remains  is  the  question 
of  general  validity  as  opposed  to  a  validity  which  is  specif- 
"  ically  sensory  or  specifically  intellectual.     How  far  is  our 


1  See  chapters  vlil  and  ix. 


184 


DEPENDENCE 


185 


intellectual  structure  satisfactory  from  a  viewpoint  which  Is 
not  merely  intellectual,  but  includes  sensory  aspects  also? 
How  far  is  our  sensuous  apprehension  valid  from  a  viewpoint 
which  includes  also  the  aspect  of  intellectual  demand? 

Dependence.— As  we  have  seen,  the  function  of  sensation 
is  to  give  us  our  starting-point.  Granted  that  every  associa- 
tion which  might  mislead  has  failed  to  do  so,  granted  that 
there  is  no  flaw  in  the  direct  apprehension  with  which  we 
see  with  our  eyes  the  corn-seeds  once  so  yellow  become  dis- 
colored, and  with  our  finger  feel  their  firmness  change  to  a 
soft  pulpiness— is  this  continuous  sensory  apprehension  all 
we  need  to  assure  us  of  the  presence  of  a  law  of  cause  and 
effect?  Can  we  state,  on  the  basis  of  an  apprehension  which 
is  merely  sensuous,  however  valid  it  may  be,  that  a  continu- 
ous sensory  sequence  is  governed  by  a  law?  Can  we  state 
that  the  visible  discoloration  and  palpable  rottenness  is  caused 
by  the  visible  and  palpable  wetness  of  the  soil? 

There  can  be  no  doubt  that  such  sensuous  observation  pro- 
vides us  with  the  evidence  by  reference  to  which  we  verify 
our  conclusion.  But  of  itself,  an  apprehension  which  is  merely 
sensuous  can  furnish  us  with  nothing  which  Is  not  itself 
sensory.  A  law  is  not  something  which  one  can  see  with 
the  eye  or  handle  with  the  fingers.  A  hypothesis  is  not 
directly  apprehensible  by  the  organs  of  taste  or  smell,  and 
consequently,  however  direct  and  accurate  sensuous  appre- 
hension may  be,  it  is  always  unable  to  give  us  direct  assur- 
ance, valid  or  invalid,  of  dependence,  whether  causal  or  logical. 
Sensation  supplies  us  with  the  material  for  reasoning,  with 
a  given  situation  from  which  we  proceed  to  Infer  and  draw 
conclusions.  But  this  basis  or  starting-point  being  given,  the 
inferring  or  reasoning  Itself  must  be  accomplished  by  ele- 
ments other  than  sensory,  and  it  is  accordingly  In  respect 
of  these  further  elements  that  we  must  ask  how  far  Inference 

is  valid. 

From  the  sensory  starting-point  described  above,  and  by 
applying  the  standards  of  Identity,  difference,  and  organisa- 
tion, I  come  to  the  conclusion  that  if  the  ground  is  continu- 
ously damp,  the  seeds  become  rotten;  that  if  the  ground  is 
not  continuously  wet,  the  seeds  develop  normally;  that  if  the 
seeds  become  rotten,  the  ground  must  have  been  unreason- 
ably damp;  and  finally,  that  if  the  seeds  develop  normally, 
we  may  be  reasonably  sure  that  the  ground  was  not  unduly 


•;l 


v/ 


186 


VALIDITY  OF  INFERENCE 


,1 

T. 

■  i  ■' 

I': 

i 

-  (■ ' 


moist.  That  is  to  say,  I  infer  ttiat  there  is  a  causal  connec- 
tion between  excessive  moisture  in  the  environment  and 
degeneration  of  the  seeds.  On  what  does  the  validity  of  this 
conclusion  depend? 

Assuming  the  mental  pattern  of  cause  and  effect,  why  do 
we  select  this  particular  cause  for  this  particular  effect? 
That  is,  why  do  we  select  from  our  sensuous  experience  just 
this  one  element — excessive  dampness  of  the  soil — as  the 
factor  which  counts?  Not  merely  because  it  is  in  accordance 
with  what  we  know  of  the  effect  of  moisture  in  general,  but 
because  such  a  supposition  fits  in  with,  and  is  supported  by, 
the  sensory  evidence  in  the  case  in  question.  It  is  satisfac- 
tory only  so  far  as  experience  bears  it  out.  If  we  could  plant 
corn  with  impunity  in  the  early  days  of  spring,  when  the 
ground  is  especially  moist,  we  should  not  accept  the  hypoth- 
esis in  question.  We  should  say,  it  sounded  well  in  theory 
but  did  not  worli  in  practice — in  other  words,  that  it  t'<ui 
not  verified  in  sensory  experience.  But  in  the  long  ru:a, 
experience  does  verify  it,  and  accordingly  farmers  wait  till 
the  damp  season  is  over  before  they  plant  their  corn. 

If,  then,  we  may  take  this  case  as  typical  of  relations  of 
dependence,  we  can  say  that  the  validity  of  inference,  in  this 
field,  depends  upon  our  introducing,  as  a  principle  of  organi- 
sation, a  mental  pattern  which  is  satisfactory,  not  merely 
to  the  intellect  with  its  general  desire  to  understand,  but 
also  to  sensory  experience,  which  presents  us  with  this  par- 
ticular situation  as  a  problem  to  be  solved.  So  far  as  the 
mental  model  is  not  only  intelligible  but  also  the  pattern  in 
accordance  with  which  the  concrete  situation  actually  seems 
to  behave — so  far  as  we  get  Insight,  not  merely  into  artificial, 
intellectual  constructions,  but  also  into  the  workings  of  the 
concrete  situation  itself — our   inference  is  valid. 

Analytical  Expansion. — Here  also  sensation  furnishes  us 
with  the  concrete  situation  from  which  we  start,  and,  of 
itself,  sensation  is  peculiarly  unable  to  analyse.  It  accepts 
intuitively,  as  a  totality,  whatever  is  given  to  it.  Here  also, 
then,  the  question  of  validity  of  inference  will  be  concerned 
mainly  in  examining  the  claims  of  our  intellectual  operations 
to  general  validity.    Let  us  take  an  example: 

"We  do  not  see  the  actual  things  themselves;  in  most  cases 
we  confine  ourselves  to  reading  the  labels  aflSred  to  them. 
This  tendency,  the  result  of  need,  has  become  even  more  pro- 


ANALYTICAL  EXPANSION 


187 


uounced  under  the  influence  of  speech;  for  words — with  the 
exception  of  proper  nouns — all  denote  genera.  The  word, 
which  only  takes  note  of  the  most  ordinary  function  and  com- 
monplace aspect  of  the  thing.  Intervenes  between  it  and  our- 
selves, and  would  conceal  its  form  fiom  our  eyes,  were  that 
form  not  already  masked  beneath  the  necessities  that  brought 
the  word  into  existence.  Not  only  external  objects,  but  even 
our  own  mental  states,  are  screened  from  us  in  their  inmost, 
their  personal  aspect,  in  the  original  life  they  possess.  When 
we  feel  love  or  hatred,  when  we  are  gay  or  sad,  is  it  really 
the  feeling  itself  that  reaches  our  consciousness  with  those 
innumerable  shades  of  meaning  and  deep  resounding  echoes 
that  make  it  altogether  our  own?  .  .  .  Mostly,  we  per- 
ceive nothing  but  the  outward  display  of  our  mental  state. 
We  catch  only  the  impersonal  aspect  of  our  feelings,  that 
aspect  which  speech  has  set  down  once  for  all  because  it  is 
almost  the  same,  in  the  same  conditions,  for  all  men.  Thus, 
even  in  our  own  individual,  individuality  escapes  our  ken."2 

Let  us  regard  this  passage  as  a  given  situation  and  proceed 
to  analyse  it.  We  select  a  single  viewpoint,  and  direct  ojr 
thought  into  a  single  channel,  taking  in  from  the  given  situ- 
ation every  element  which  is  of  significance  for  this  viewpoint, 
and  omitting  or  rejecting  everything  which  is  irrelevant.  Let 
us  take  for  our  first  aim,  to  make  a  lis.,  of  everything  which 
is  stated  or  clearly  implied  about  "Things." 

Things  are  other  than  we  see  them — are  more  than  the  labels 
which  are  attached  to  them — have,  in  addition  to  the  super- 
ficial aspects,  aspects  which  are  profound,  unusual,  unfamiliar 
— aspects  of  a  deeper  nature  which  is  beyond  naming,  and  is 
profoundly  individual — which,  to  be  apprehended  as  It  Is, 
must  be  regarded  from  some  viewpoint  which  goes  beyond 
merely  practical  interests,  etc. 

So  too  with  our  innermost  feelings.  Like  things,  these  have 
an  intrinsic  essence,  a  life  and  individuality  of  their  own, 
infinitely  more  profound  than  the  superficial  aspects  which 
do  duty  for  every-day  purposes.  If  we  wish  to  grasp  them 
in  their  true  individuality,  we  must  use  some  method  differ- 
ent from  discursive  thought,  which  seizes  only  upon  aspects 
which  are  general,  and  can  be  expressed  by  names. 

Then  again  we  can  take  our  own  knowledge.    We  are  thor- 

*  After  Rergson,  Etioy  on  Laughter. 


I 


188 


VALIDITY  OF  INFERENCE 


'  i 


oughly  practical,  in  science  no  less  than  in  ordinary  life.  We 
grasp  at  the  easiest,  most  superflcial  aspects  of  things  and  of 
our  selves,  being  satisfied  with  what  will  worlc  for  practical 
purpose.  We  are  driven  to  do  this  by  the  pressure  of  prac- 
tical necessil.es,  and  as  an  aid  to  this  kind  of  life  have 
invented  language — general  ex.^ressions  which  come  between 
us  and  ultimate  realities,  until  we  have  come  to  live  in  a 
world  of  mental  fictions,  general  concepts  which  we  can  use 
for  scientific  purposes,  but  which  conceal  from  us  the  vital 
essence  of  our  selves  no  less  than  of  things. 

So  too,  we  might  pay  especial  attention  to  language,  or  to 
individuality,  etc.,  or  to  the  interconnection  of  these  concepts, 
and  so  make  one  element  in  the  passage  after  another  the 
subject  of  a  detailed  study,  until  every  single  element  had 
been  considered  in  turn  and  nothing  had  been  omitted.  In 
this  way  the  whole  passage  would  have  been  analysed  and 
expanded. 

Regarding  this  instance  as  typical  of  the  work  of  analysis, 
let  us  proceed  to  ask  how  far  such  procedure  Is  legitimate. 
The  end-point  is  very  different  from  the  starting-point.  We 
have  taken  each  element  out  of  its  given  context,  have  placed 
together  in  a  new  context  elements  taken  from  different  parts 
of  the  passage,  in  such  a  way  that  they  seem  to  throw  upon 
one  another  a  light  which  is  new.  At  any  rate,  the  patterns 
according  to  which  the  passage  has  been  analysed  and  the 
results  classified  together  in  the  above  groups,  were  Introduced 
by  us  in  analysing,  and  it  may  well  be  questioned  how  far 
such  interference  with  contexts  is  legitimate.^ 

That  such  procedure  adds  to  our  insight,  is  certain.  The 
new  patterns  of  arrangement,  the  taking  one  point  at  a  time, 
the  putting  together  every  item  of  meaning  which  refers  to 
one  and  the  same  point,  is  undoubtedly  helpful  in  Introducing 
clearness  and  intelligibility  into  the  given  passage.  The  only 
question  which  rises  in  our  minds  is,  whether  our  procedure 
is  not,  perhaps,  after  all  subjective,  a  mental  luxury  which 
makes  our-convenience-in-understanding  the  first  thing  and  Is 
unjust  to  the  passage — or  whether  our  analysis  has  an  objec- 
tive significance.  There  is  no  doubt  that  such  tampering  with 
contexts  is  sometimes  illegitimate.  Under  the  Influence  of 
political  or  personal  feeling,  men  analyse  each  other's  utter- 


3  Cf.  Bradley,  Principles  of  Logic,  pp.  499-500. 


ANALYTICAL  EXPANSION 


189 


ancea  in  a  way  which  makes  sufficiently  clear  to  theinielve§ 
how  base  are  the  intentions  of  the  other  party.  But  it  is 
well  knowii  how  biased  and  unreliable  such  analyses  are. 
Analysis,  then,  may  be  biased  or  possibly  unbiased,  and  may 
be  reliable,  or  possibly  unreliable.  What  is  to  be  our  crite- 
rion? How  are  we  to  know  when  an  analysis  is  reliable,  and 
when  it  is  not? 

The  answer  is  plain.  Analysis  is  to  be  trusted,  when  it  is 
the  analysis  of  the  given  situation,  when  the  substitution  of 
one  context  for  another  makes  clearer  a  meaning  which  li 
already  there,  but  is  not,  perhaps,  so  clearly  expressed.  Tak- 
ing one  point  after  another  is  Justified,  so  far  as  such  a 
method  makes  intelligible  the  sense  of  the  given  passage.  If 
it  throws  light  upon  the  datum,  and  makes  clear  the  Intellectual 
context  of  the  concrete  situation  Itself,  any  such  procedure  Is 
thoroughly  justified.  If  however  the  introduction  of  new 
angles  of  approach  obscures  or  falsifies — as  prejudice,  for 
example,  obscures  and  falsifies — It  is  illegitimate.  The  veri- 
fication, then,  of  an  analysis  Involves  patient  and  constant 
reference  to  the  given  material — reference  at  each  forward 
step,  as  well  as  at  the  final  conclusion,  and  at  the  final  con- 
clusloi  as  well  as  at  each  forward  step.  Only  thus  can  we  be 
certain  that  the  introduction  of  the  intellectual  standards  of 
Identify,  difference,  and  organisation  is  satisfactory  to  our  sen- 
sory, as  well  as  to  our  intellectual,  apprehension. 

This  seems,  perhaps,  so  simple  as  to  be  hardly  worth 
stating.  And  yet,  everywhere  one  looks,  one  finds  examples 
of  what  to  avoid.  Without  the  most  patient  and  continuous 
reference  to  the  given  situation,  the  most  Ingenious  and  per- 
sistent attempts  at  analytical  expansion  serve  only  to  divert 
from  the  path  and  ti  lead  to  constructions  which  are  built 
upon  no  reliable  foundation.  The  student  who  Is  familiar 
with  modem  attempts  at  Shakespearean  itterpretatlon  is 
well  aware  that  many  of  the  attempts,  literary  as  well  as 
psychological,  evince  the  utmost  subtlety  of  analysis,  the  most 
rigid  and  patient  following  out  of  one  path  at  a  time.  And 
yet,  sometimes  half-way  through,  and  almost  always  at  the 
end,  the  reader  of  these  novel  explanations,  while  forced  to 
admire  the  analytical  dexterity  and  logical  or  psychological 
acumen  of  the  critic,  and  the  extreme  clearness  and  fascinat- 
ing persuasiveness  of  his  mental  patterns,  is  forced  also  to 


11 

ii 

1 11 


\90 


VALIDITY  OF  INFERENCE 


I  ■ 


it 


ask  himself — can  this  poaalbly  be  Shakespeare?  Only  too 
often  the  answer  is  In  the  negative. 

The  validity  of  analytical  expansion,  then,  is  determined 
In  the  last  resort,  not  merely  by  applying  standards  which 
satisfy  the  Intellectual  demand  for  clearness  and  consistency 
of  outlook,  but  also  by  reference  to  the  concrete  situation 
from  which  we  started.  Only  so  far  as  the  meaning  which 
our  methods  succeed  in  extracting  from  the  material  is  the 
meaning  of  the  situation  Itself,  is  our  analysis  verifiable  and 
accepted  as  legitimate. 

Novelty. — The  persistent  application  of  methodical  infer- 
ence usually  results  in  an  insight  which  reveals  something 
novel,  discovers  something  new,  or  at  least  previously 
unnoticed.  By  putting  two  and  two  together,  we  discover 
something  which  otherwise,  perhaps,  would  have  escaped  our 
most  careful  scrutiny — such  as  the  age  of  a  new  minister, 
some  vexed  problem  ot  authorship,  or  the  solution  of  some 
historical  problem,  for  example,  the  question  as  to  the  pass 
by  which  Hannibal  crossed  the  Alps.  By  the  careful  and 
methodical  analysis  of  a  complex  situation,  we  discover  some- 
thing which  would  otherwise  have  been  missed  by  that  super- 
ficial acquaintance  which  does  duty  for  every-day  purposes. 
By  the  simple  extension  of  something  which  we  already  know, 
we  may  make  discoveries  of  enormous  importance  for  our 
whole  future  development.  To  the  student  who  can  at  last 
read  a  hundred  lines  of  the  Aeneid  in  an  hour,  it  occurs,  with 
something  of  a  mental  shock,  that  he  can  read  two  hundred 
lines  in  two  hours,  or,  further,  that  since  there  are  only 
between  seven  and  eight  hundred  lines  in  the  average  book, 
he  can  read  a  whole  book  in  a  single  day,  or  even — illuminat- 
ing and  inspiring  thought! — the  whole  Aeneid  in  less  than  a 
fortnight.  To  the  student  who  has  been  accustomed  to  spend- 
ing the  greater  part  of  a  term  over  a  single  book,  this  exten- 
sion of  what  he  already  knows  comes  with  all  the  force  of 
novelty,  and  is  the  source  of  a  new  insight  which  may  alter 
his  whole  future  plans  of  study,  and  indeed  may  affect  radi- 
cally his  choice  of  a  profession. 

How  far  is  such  novelty  trustworthy?  It  is  by  analysis,  by 
extension,  or  by  putting  two  .ind  two  together,  th.it  we  make 
discoveries  of  this  kind,  and  it  is  so  far  as  these  methodu — 
of  analysis,  extension,  and  construction  of  systems — are  valid, 
that  their  results  can  be  accepted  without  misgiving.     The 


NOVELTY 


191 


caM  of  analysis  we  have  already  discussed,  and  at  the  prMwnt 
stage  we  can  say  definitely  tbat  so  far  ai  our  intellectoal 
operations  upon  the  given  material  result  in  unearthing  some- 
thing which  was  already  there,  present  In  the  concrete  situa- 
tion but  unnoticed,  so  far  such  inferences  are  sufficiently 
reliable.  The  case  of  extension  and  const  ^ction  of  systems 
will  be  left  for  the  next  section,  but  at  present  we  can  say 
tbat  so  far  as  such  extensions  are  legitimately  involTed  in 
the  concrete  situation — i.  e.,  so  far  as  they  follow  reasonably 
upon  what  is  given— they  are  to  be  trusted,  and,  in  general, 
our  conclusion  is  that  Inferences  which  result  in  new  discov- 
eries are  valid  so  far  as  they  bring  to  light  something  which 
was  already  present,  or  is  logically  Implied  by  what  is  present, 
in  the  given  situation  from  which  we  start. 

Constructlveness.— Inference  is  constructive.  If  a  some- 
what lengthy  package  is  delivered  to  our  neighbor  from  a 
delivery  van  with  the  sign  "Sporting  Qoods,"  and  we  see  our 
neighbor  digging  in  his  garden  for  worms  that  evening,  any 
reasonable  person  will  reconstruct  for  himself  the  scene  which 
is  to  be  enacted  the  following  morning,  and  the  part  which 
will  be  played  by  the  contents  of  the  package — even  though 
he  is  witi<  ->ut  special  knowledge  of  his  neighbor.  If  a  psycho- 
analytl  xamination  reveals  undue  hesitation  in  reacting 
to  the  St  ulus-words  "Ring,"  "Woman,"  "Marriage,"  "Voyage," 
etc.,  we  should  draw  our  own  conclusions  as  to  the  state  of 
mind  of  the  subject,  and  could  reconstruct  certain  of  his  chief 
Interests  and  portions  of  bis  recent  history  with  fair  accu- 
racy, even  though  we  had  lever  seen  him  before.  So  too  from 
a  few  scattered  notices  taken  from  the  works  of  ancient  critics, 
a  modern  scholar  will  reconstruct  the  outlines  of  a  lost  play 
by  Euripides  or  Menander,  much  in  the  same  way  as  from  a 
few  bones  an  anatomist  will  reconstruct  a  mammoth  or  eohip- 
pus,  or  an  anthropologist  will  reason  from  the  disposition 
of  the  remains  of  a  pre-historic  man  that  he  had  a  religion 
and  believed  in  the  immortality  of  the  soul.4 

What  are  we  to  say  as  to  the  validity  of  such  inferential 
constructions?  They  are  all,  of  course,  hypothetical,  and  none 
of  them  are  absolutely  certain.  But  when  we  thus  go  boyond 
the  Immediately  present  facts  and  enlarge  upon  our  data, 
regarding  them  as  fragments  of  some  greater  hypothetical 


«Cf.  K.  R.  M&rett,  AnthropolOffy,  p.  20C. 


192 


VAUDITY  OF  INFERENCE 


If' 
if 


t 


■yit«in,  la  our  procedure  bo  reliable  u  to  be  beyond  reaionable 
■uipicion?  I^t  us  consider  what  we  do  In  making  such  con- 
structions. We  analysp  the  concrete  situation  which  is  glrsn 
to  us,  take  it  apart  into  its  elpinents,  intensify  the  Identity 
and  difference  aaperts  of  these  elements  until  they  can  be 
used  aH  mental  countorH,  rontextless  or  almost  rontextless 
entitles  which  can  be  put  together  In  accordance  with  almost 
any  Intellectual  pattern,  until  we  end  up  with  a  mental  model 
which  we  can  take  apart  and  put  together  again  with  fair 
insight  Into  the  principle  in  accordance  with  which  we  hare 
constructed  it.  Instead  of  the  concrete  situation  with  which 
we  started,  we  have  an  almost  contextless  artefact,  intelligible 
Indeed,  but  connected,  at  best,  only  remotely  with  the  facts 
of  sensory  experience  with  which  we  started.  How  far  ii 
this  Inferential  procedure  to  be  accepted  as  reliable? 

That  such  systems  are  at  times  far  from  trustworthy.  Is 
beyond  doubt.  From  the  paranoiac  or  the  adolescent  who  sees 
everyone  in  a  conspiracy  against  him,  to  the  optimist  who 
sees  everything  without  exception  working  wholly  for  his  best 
in  this  best  of  all  possible  worlds,  the  products  v  <  itellectual 
construction  do  not  escape  a  certain  suspicion,  id  even  in 
the  sphere  of  scientific  research,  many  a  brilliant  theory  has 
been  discarded,  as  going  too  far  beyond  the  evidence.  N-rays 
whose  "faint  luminosity"  is  invisible  to  everyone  except  their 
discoverer,"'  Phlogiston,  the  Geo-centric  view  of  astronomy — 
how  many  doubtful  hypotheses  have  been  constructed  in  the 
tragi-comedy  unfolded  in  the  history  of  culture?  What  is 
it,  then,  which  makes  us  trust  one  construction,  and  regard 
another  system  as  wholly  unreliable? 

Let  us  consider.  In  the  case  of  rival  hypotheses — different 
and  opposed  theories  to  account  for  the  same  group  of  phenom- 
ena— on  what  basis  do  we  make  our  choice?  For  example, 
do  plants  grow  upwards  because  they  love  the  sun,  or  because 
they  have  a  special  organ  analogous  to  the  statocyst  in  the 
animal  kingdom?  That  is  to  say,  is  the  explanation  of  their 
growth  to  be  in  terms  of  a  simple,  unmediated  hellotropism, 
or  in  terras  of  a  more  complex  organ  for  appreciating  the  influ- 
ence of  the  earth's  gravity?  Or,  if  perhaps  both  factors  are 
present,  which  plays  the  greater  part?  There  is  only  one 
way  to  find  out  with  reasonable  certainty.     We  must  devise 


'llr 


»  Ct.  Goblot,  Traite  de  Logtque,  pp.  49-50. 


■'0 


THEORY  OF  INFERENCE 


«xperimenta  which  will  bring  only  one  factor— <•.  g.,  gr«TiU- 
tlon— Into  play  at  a  time,  and  see  how  our  test-Bpeclmena  actu- 
ally behave.  We  muiit  alio  fliBsect  a  reasonable  number  of 
plants,  and  And  out  whether  there  1h  present  anatomical  evi- 
dence of  the  complex  organs  in  question.  That  la  to  say,  we 
can  choose  between  rival  hypotheses,  or  for  that  matter  verify 
a  single  hypothesis,  only  by  careful  study  of  the  concrete 
situation  Itself,  in  order  to  discover  whether  the  suggested 
system  Is  present  In,  or  implied  In,  the  data.  If  the  sug- 
gested explanation  Is  Intellectually  satisfactory — i.  «.,  If  w« 
can  take  the  mental  model  to  pieces  and  put  It  together  again 
with  a  reasonable  degree  of  insight  Into  the  law  of  Its  con- 
struction—the only  question  as  to  its  validity  Is,  whether  It 
is  or  Is  not  a  system  present  in,  or  Implied  in,  the  data.  If 
it  proves  to  be  the  system  of  the  concrete  situation,  then  we 
can  regard  our  reconstruction  as  an  explanation  of  the  data, 
and  If  it  Is  In  accordance  with  all  that  Is  known  In  that  par- 
ticular field,  we  tend  to  regard  the  explanation  as  to  be 
accepted.  Validity,  then.  In  the  construction  of  systems, 
depends  wholly  upon  whether  the  I»itellectual  context  which 
we  thus  construct  proves  to  be  the  Intellectual  context  of  the 
data  themselves,  or  at  least  a  reasonable  extension  of  such 
context. 

Conclusion — The  Theory  of  Inference.— In  this  way  we  come 
to  realise  that  the  theory  of  Inference  and  the  theory  of  Judg- 
ment are  one  and  the  same.  The  movement  of  our  thought, 
whether  In  judgment  or  In  Inference,  If  It  Is  to  be  regarded  as 
valid,  must  satisfy  certain  conditions.  It  starts  with  a  datum, 
a  concrete  situation  with  which  we  are  In  touch  largely  by 
means  of  sense-perception.  This  datum  it  analyses  and 
remodels  until  It  Is  shaped  more  In  accord  with  intellectual 
demands — i.  e.,  until  the  Intelligible  elements  In  the  given 
situation  which  are  relevant  to  our  special  viewpoint  are 
placed  in  their  proper  intellectual  setting,  so  that  their  Inter- 
relation can  be  sufficiently  understood.  The  validity  of  such 
thought-activities  depends  wholly  on  whether  the  operations 
of  sense-perception  and  of  Intellectual  reconstruction  are  per- 
formed accurately,  not  merely  In  themselves,  as  taken  singly 
and  separately,  but  as  taken  together,  with  especial  reference 
to  each  other.  Bach  single  step  of  the  process,  from  the  first 
sensory  apprehension  to  the  last  remodelling  In  the  Intellect, 
should   be   verifiable   by   explicit    reference   to   the   concrete 


194 


VALIDITY  OF  INFERENCE 


datum,  anl  each  element  of  sensuous  apprehension  should  be 
purifled  from  carelessness  and  misleading  associations  by  a 
critical  attitude  which  ensures  as  close  conformity  to  intel- 
lectual standards  as  the  nature  of  the  case  admits. 

FOR  FURTHER  READINO 

P.  H.  Bradley,  Prin<-iples  of  Logic,  Bk.  Ill,  Part  II,  chapters  lli-lv. 
Chr.  Slgwart,  Loaic.  Vol.  11,  pp.  5-23,  464-480.  W.  Wundt,  Logik. 
(3rd  Edit.),   Vol.  I,  pp.  302-308. 


EXERCISES 

On  what  does  the  Talldlty  of  the  following  inferences  depend:  (1) 
A  sailor,  coasting  along  the  shore  of  an  unknown  land,  one  morning 
notices  that  he  Is  passing  scenery  which  he  passed  four  days  before 
— and  Infers  that  the  unknown  land  must  be  an  Island.  (2)  Writers 
of  almanacs  tell  us  beforehand  when  eclipses  are  to  take  place.  This 
has  been  Inferred.  (3)  We  leave  home  In  the  morning,  and  Infer 
that  when  we  return   In  the  evening  our   home   will  still   be  there. 

4.  We  place  a  letter  on  our  private  mall  box,  and  after  a  few  hours, 
notice  that  It  Is  no  longer  there.  We  infer  that  the  postman  has 
taken  It.  (5)  vVe  lock  out  of  the  window  in  the  morning,  and  see 
the  ground  white  with  frost.  We  infer  that  the  tomato  plants  have 
been  killed.  (6)  We  read  in  the  paper  that  Mr.  X  has  been  elected 
president,  and  Infer  that  this  statement  Is  true.  (7)  We  look  at  the 
clock  and  find  that  it  indicates  an  absurdly  impossible  time.  We 
infer  that  we  must  have  forgotten  to  wind  it.  (8)  We  read  In  the 
paper  "Wanted,  a  man  to  drive  a  team  with  religious  views,"  and 
Infer  that  a  comma  must  have  dropped  out.  (9)  We  listen  to  a  piece 
of  music,  and  infer  tha*'  it  must  have  been  composed  by  Beethoven. 
(10)  We  infer  that.  It  we  continue  to  work  hard  along  the  lines 
which  interest  us,  we  shaM  certainly  be  successful  in  the  end? 


PART  III 


SCIENTIFIC  METirlCD 


195 


i! 


'  1 


CHAPTER  XVIII 


GENERAL    JHARACTERISTICS  OF  SCIENTIFIC  METHOD 


Unscientific  and  Scientific  Method. — A  and  B  have  each  a 
business  in  the  same  town.  A  has  three  clerks,  and  each 
clerk  does  what  he  can.  During  the  busy  part  of  the  day, 
every  one  keeps  busy  attending  to  customers,  but  during  the 
slack  times,  when  there  is  less  to  do,  less  is  done.  Each 
clerk  knows  as  much  about  the  business  as  the  others,  and 
any  one  of  them  is  ready  to  do  anything,  from  buying  in  goods 
to  answering  the  telephone.  B  has  three  clerks,  but  their 
work  is  more  specialised.  B  does  the  buying  in  himself,  and 
each  of  his  clerks  has  his  definite  department.  His  store 
seems  to  be  kept  more  neatly,  and  while  none  of  his  clerks 
seem  to  have  as  wide  knowledge  about  the  business  as  A's 
clerks,  each  one  knows  a  great  deal  more  in  his  own  particu- 
lar department.  When  business  is  slack,  his  clerks  are  tabu- 
lating and  classifying  the  goods  in  their  own  departments, 
and  during  the  busier  part  of  the  day  it  takes  them  less  time 
to  do  business  than  at  A's  store,  because  each  knows  exactly 
what  he  has  in  his  own  department,  and  can  put  his  hand  on 
it  at  once.  In  two  years'  time,  A  is  going  out  of  business,  while 
B  is  enlarging  his  premises. 

C  and  D  are  students  in  the  same  college.  G  attends  classes 
and  reads  his  assignments  in  a  general  sort  of  way,  but  does 
not  get  much  out  of  his  course.  He  takes  things  as  they 
come  along.  If  he  happens  to  understand  a  subject  easily, 
he  passes.  If  there  is  any  difficulty,  he— stakes  another  subject. 
D  puts  in  no  more  time  on  his  work  than  C,  but  he  goes  about 
it  in  a  different  way.  He  takes  notes  of  what  seems  impor- 
tant in  class,  and,  in  preparing  his  assignments,  makes  brief 
analyses,  noting  down  the  important  points  and  running  them 
over  before  class.  He  soon  learns  what  sort  of  thing  to  look 
out  for,  and  has  little  difficu'ty  in  mastering  each  subject  he 
takes  up.  Finally,  he  elects  courses  which  belong  together 
and  give  him  what  he  wants  to  get  from  his  college  work. 
At  the  end  of  his  course,  he  has  developed  a  great  deal,  while 

197 


198    CHARACTERISTICS  OF  SCIENTIFIC  METHOD 


-t 


C  leaves  college  without  a  degree  and  with  a  marked  distaste 
for  study. 

These  instances  illustrate  the  difference  between  drifting 
along  in  a  general  sort  of  way,  and  applying  scientific  method. 
It  is  the  difference  between  blundering  along  with  a  trial-and- 
error  method,  and  flnding  one's  way  with  a  trial-and-success 
method.  There  is  a  right  way  and  a  wrong  way  of  doing 
anything.  The  right  way  is  the  efficient  way  which  leads 
to  success.  The  wrong  way  is  the  inefficient  way  which  leads 
to  failure.  What  is  called  "scientific  method"  has  arisen  from 
a  study  of  the  methods  which  "work,"  that  is  to  say,  which 
lead  to  success.  Such  methods  have  been  studied  in  commerce, 
in  art,  in  the  technical,  applied  sciences,  and  above  all  in  the 
laboratories  in  which  genuine  discoveries  have  been  made. 
Efficient  methods  of  salesmanship  differ  from  efficient  methods 
of  using  tools,  and  efficient  methods  of  using  tools  differ  again 
from  the  efficient  methods  by  which  the  original  thinker  solves 
his  problems.  Each  branch  of  work  has  its  specialised  appli- 
cation of  met.t  Is  found  valuable  for  its  special  purposes. 
But  it  has  been  found,  in  spite  of  these  differences  of  detail, 
that  there  are  a  number  of  general  respects  in  which  all  such 
methods,  whatever  the  branch  of  work,  agree.  It  is  the  sys- 
tematic study  of  these  general  characteristics  of  scientific 
method  which  will  be  dealt  with  in  the  remainder  of  this 
book. 

What  are  the  most  general  characteristics  of  scientific 
method,  the  characteristics  which  all  successful  workers  in 
every  field  agree  in  regarding  as  important?  If  we  ask,  what 
the  method  is,  rather  than  how  it  should  be  applied,  we  find 
that  it  has  two  functions  which  are  most  generally  consid- 
ered of  importance.  (1)  Certain  methods  are  concerned  with 
investigation,  discovery,  flnding  out  something  new.  (2) 
Certain  others  are  concerned  with  exposition,  explaining  to 
others,  organising  what  we  already  know.  Investigation,  then, 
and  Exposition  are  the  two  functions  of  scientific  method  which 
are  most  generally  regarded  as  important.  Application  comes 
only  after  the  demands  of  science  in  the  way  of  investigation 
and  in  the  way  of  exposition  have  been  satisfied. 

Methods  of  Investigation  (A)  Analysis. — What  are  the  chief 
methods  employed  in  investigation?  The  very  first  is  analysis. 
Before  we  can  solve  any  problem  which  is  at  all  complex,  it 
is  necessary  to  take  stock,  as  it  were,  both  of  what  we  know 


METHODS  OF  INVESTIGATION 


199 


and  of  what  we  do  not  know  but  have  to  find  out,  with  explicit 
reference  to  thp  case  before  us.  One  of  the  very  first  things 
which  a  recruit  learns  to  do  with  his  rifle  is,  to  take  it  to 
pieces.  One  of  the  first  things  which  a  research  scientist  has 
to  do,  is  to  analyse  his  problem  and  tabulate  his  data.  One 
of  the  first  things  which  a  physician  has  to  do  If,  to  make  a 
list  of  the  symptoms  of  the  patient  to  whom  he  is  called. 
Before  any  steps  of  a  more  advanced  kind  can  be  taken 
towards  solving  a  problem,  it  is  necessary  to  realise  exactly 
what  the  problem  is,  what  are  its  conditions,  or — as  the 
scientist  puts  it — what  are  the  data.  This  first  step  which 
is  preliminary  to  all  further  work  upon  a  problem,  whatever, 
the  field  and  whatever  its  specialised  name — as  diagnosis,  tak* 
ing  stock,  tabulating  data,  etc., — is,  in  its  essential  nature, 
analysis. 

(B)  Abstraction. — A  second  general  method  of  investigation, 
analytical  in  its  nature  and  following  closely  upon  the  pre- 
liminary analysis  just  mentioned,  is  the  method  of  abstraction. 
Given  the  analysis  of  a  concrete  situation  into  its  general  ele- 
ments, it  is  usually  necessary  to  pick  out  certain  of  these 
elements,  and  set  on  one  side,  as  Irrelevant  or  at  least 
negligible,  certain  other  elements,  all  of  which  were  equally 
present  in  the  concrete  situation  with  which  our  analysis 
dealt.  This  process  of  picking  out  from  the  data  those  ele- 
ments whicb  are  important  for  some  special  purpose,  and 
neglecting  the  others,  is  a  method  uf  isolation.  By  its  means, 
we  isolate  a  special  group  of  elements  for  special  investiga- 
tion, and  are  thu3  enabled  to  concentrate  our  attention  upon 
the  problem  bit  by  bit,  instead  of  having  to  deal  with  it  as 
a  whole.  "Divide  and  conquer'  Is  true  not  only  in  military 
science,  but  in  all  scientific  study;  and  this  process  by  which 
we  isolate  certain  elements  so  that  we  can  solve  the  problem 
piece-meal,  is  abstraction.  As  an  example  of  this  method  at 
work,  we  can  consider  the  way  in  which  geometry,  which  deals 
with  the  nature  of  space,  does  not  attempt  to  study  spacb 
as  a  whole,  but  splits  up  the  problem,  and  begins  with  a 
study  of  two-dimensional  space,  especially  with  a  study  of  the 
properties  of  straight  lines,  triangles,  circles,  parallelograms, 
etc.  So  too  Aristotle,  in  writing  upon  the  subject  of  Friend- 
ship, does  not  deal  wi'.i  the  whole  question  In  a  geaeral  way, 
but  divides  It  up  into  friendships  of  pleasure,  friendships  of 
business,  etc.,  and  discusses  each  of  these  in  abstraction  from 


200    CHARACTERISTICS  OF  SCIENTIFIC  METHOD 


Mi 


i: 
I. 


the  othors.  By  this  method  he  is  enabled  to  introduce  a 
degree  of  clearness  and  distinctness  into  his  discuRsion  which 
is  the  admiration  even  of  present-day  thinlcers.i 

(C)  Determination. — A  third  general  method,  following 
closely  upon  the  isolating  method  of  abstraction,  is  the  method 
of  determination.  Given  a  narrow  group  of  isolated  elements, 
a,  b,  c,  d,  .  .  .  it  is  possible  to  proceed  further  by  a  care- 
ful comparison  of  a  with  b,  c,  d,  .  .  .  resulting  in  what 
are  called  new  "determinations"  of  a.  When  friendship  has 
been  analysed  into  the  special  groups  of  friendships  based 
upon  community  of  purpose  in  some  higher  sense,  as  In  moral, 
educational,  or  scientific  collaboration,  it  is  possible  to  "deter- 
mine" each  of  these  groups  further  by  comparing  Instances 
viewed  in  varying  circumstances.  They  can  be  compared  in 
respect  of  durability,  in  respect  of  ethical  value,  in  respect 
of  their  value  for  science  or  art.  In  respect  of  economic,  social, 
or  religious  value,  etc.,  and  each  comparison  tends  to  bring 
out  new  determinations,  until  in  the  end  we  know  far  more 
about  both  elements  and  groups — and  indeed  about  friendship 
in  general  too — than  we  did  before  this  method  was  applied. 
This  method,  then,  which  appears  to  be  less  of  an  analytical, 
and  more  of  a  synthetical  nature,  is  known  as  determination.2 
It  leads  to  definition  and  classification,  though  these  are  usu- 
ally regarded  as  coming  under  Exposition  rather  than 
Investigation. 

(D)  Synthesis. — A  fourth  g&neral  method  of  investigation 
is  synthesis.  The  word  synthesis  means  putting  together, 
and  it  may  be  the  precise  reverse  of  analysis,  as  when  the 
recruit  who  has  taken  his  rifle  to  pieces  is  taught  to  put  It 
together  again  by  exactly  reversing  the  order  of  procedure 
by  which  he  took  it  apart.  But  an  exact  reversal  of  the 
analytical  procedure  is,  in  actual  fact,  somewhat  rare.  It 
is  far  more  usual  to  take  the  elements  which  analysis  and 
abstraction  have  set  before  us,  and  to  put  these  together  in 
some  order  which  is  new.  We  may  omit  certain  of  the 
elements  originally  present,  on  the  ground  that  they  are  irrel- 
evant and  unnecessary,  and  much  of  the  value  of  synthesis 


1  See  Aristotle's  Niconuachean  Ethics,  Bka.  vlil-lx,  and  the  introduc- 
tory remarks  of  Sir  Alexander  Grant,  In  his  edition,  ImmpdiatelT  before 
the  beginning  of  Bk.  VIII.  ' 

2  The  meaning  and  value  of  Determination  arc  especially  treated  of 
by  John  Locke,  In  the  second  edition  of  the  Essau.  See  Frasw's 
edition  of  the  Eaiay,  pp.  22-24 


METHODS  OF  INVESTIGATION 


201 


as  a  scientific  method  consists  in  its  use  in  experimentally 
discovering  Just  what  may  be  omitted  without  prejudicing 
the  result.  White  light  is  analysed  into  a  mixture  of  various 
wave-lengths  of  ether,  but  we  can  synthetically  produce  the 
appearance  of  white — e.  g.,  on  the  color-wheel — oy  mixing,  not 
all  the  rays  of  the  spectrum,  but  as  few  as  three  or  even  two 
of  the  spectral  colors  revealed  by  analysis. 

Further,  by  using  the  point,  straight  line,  and  surface 
revealed  by  analysis,  synthetic  geometry  can  construct  any 
number  of  mathematical  forms  which  are  of  the  utmost 
Importance  for  progress,  not  merely  in  geometry  itself,  but 
in  all  the  sciences  which  admit  of  the  application  of  "eo- 
metrical  methods.  That  is  to  say,  synthesis  is  by  no  means 
limited  to  the  concrete  situation  from  which  analysis  started, 
but  can  go  beyond  it  in  its  new  constructions,  creating  forms 
l.'iie  the  eikosihedron,  which  is  not  found  in  nature,  and  such 
ideas  as  a  fourth,  fifth,  or  nth  dimension  of  space,  which  is 
not  observed  by  us .3  Synthesis,  then,  Is  valuable  in  at  least 
three  distinct  ways:  (1)  It  may  be  used  as  a  check  upon 
analysis,  as  when  we  verify  analytical  results  by  reconstruct- 
ing the  concrete  situation.  (2)  It  may  be  used  in  the  dis- 
covery of  simpler,  more  economical  or  more  efficient  methods 
of  producing  a  desired  result,  as  synthetic  chemistry  con- 
structs substitutes  for  natural  products  which  are  hard  to 
obtain.  (3)  It  may  be  used,  as  in  mathematical  construc- 
tions generally,  to  give  us  information  which  reaches  far 
beyond  our  original  data,  as  we  see  especially  in  the  use  of 
graphs.  This  third  use,  however,  is  not  by  any  means  con- 
fined to  mathematical  constructions,  but  is  true  generally, 
as  every  applied  science  bears  witness. 

(D)  Synthetical  Abstraction  and  Determination. — ^A  sub- 
form  of  abstraction  is  largely  of  a  synthetical  nature.  There 
is,  in  addition  to  the  abstraction  which  isolates  elements,  an 
abstraction  which  Isolates  laws  or  generalisations  from  experi- 
ence. It  is  by  the  aid  of  this  generalising  abstraction  that 
we  neglect  the  particular  and  accidental  element  in  individual 
experiences,  and  select  for  especial  attention  the  general  or 

3  Such  symbolic  extenslong  of  Ideas  orlKlnally  fciven  In  sense-experi- 
ence, are  what  Locke  calls  "Modes."  Slirple  Modes  are  expansions 
of  a  itiugle  Idea,  as  2,  3,  4,  &.  are  expa^ions  of  the  arithmetical 
unit,  and  Comiplex  or  Mixed  Modes  are  formed  by  nnitlng  difTerent 
Ideas,  or  their  expansions,  ~<^  "rannlng"  Is  a  '*ompoeite,  consisting  of 
(1)  complex  movements  ami  (2)  the  sense  o..  power.  Cf.  Ba»ay,  Bk. 
II,  chapters  xvlii,  xxii. 


i 


P' 


iil 


202    CHAF^ACTF.RISTICS  OF  SCIENTIFIC  METHOD 

more  universal  element.  This  may  look  as  though  we  were 
isolating  the  law-aspect  of  our  exporienceB,  and  consequently, 
as  though  the  method  of  generalising  abstraction  were  really 
analytical.  In  practise,  however.  It  always  represents  a  sum- 
ming up  of  many  experiences,  and  is  thus  synthetical.  A 
composite  photograph,  for  example,  is  formed  by  putting 
together  many  negatives  in  order  to  obtain  a  single  positive. 
The  final  positive  brings  out  all  the  elements  which  the 
different  negatives  had  in  common,  and  omits  the  elements 
which  appear  in  only  one  or  two  negatives.  In  this  way  we 
obtain  a  type-form,  and  it  is  obtained  by  abstraction.*  But, 
as  resulting  from  many  negatives  and  summing  them  up, 
such  generalised  products  of  abstraction  are  synthetical,  much 
as  a  graph — such  as  the  practlse-curve,  or  the  memory-curve 
— sums  up  the  results  of  many  experiences  and  is  usually 
regarded  as  synthetical.  That  "determination"  is  largely 
synthetical,  we  have  already  stated.  These  methods  of  gen- 
eralising abstraction  and  determination  lead  naturally  to 
classification,  but  this  is  gf  "rally  treated  under  the  head  of 
Exposition. 

(E)  Induction.— A  fifth  method  of  investigation,  which 
depends  upon  both  analysis  and  synthesis  in  all  their  forms, 
is  induction.  By  some  logicians  induction  is  regarded  as  the 
investigatory  method  par  excellence.  But  there  can  be  little 
doubt,  from  a  modern  viewpoint,  that  it  is  a  special  form 
wnich  presupposes  both  analysis  and  synthesis.  A  just  crit- 
icism frequently  leveled  at  Mill's  "inductive  methods"  objects 
that  when  phenomena  are  already  analysed  into  A,  B,  C,  etc., 
— as  in  his  exposition  is  always  talten  for  granted — the  real 
work  of  investigation  is  almost  completed  before  the  specif- 
ically inductive  methods  are  brought  into  play;  and  in  gen- 
eral, there  can  be  no  doubt  that  analysis  and  synthesis  are 
more  general  methods,  methods  of  wider  application,  and 
that  induction  proper  is  somewhat  more  narrow  and  specific, 
and  presupposes  both  analysis  and  synthesis."'  The  typically 
inductive  method  starts  from  a  concrete  situation  which  tias 
already    been    analysed    and    further    prepared    by    isolating 

*  Cr    Fr.   Galton,  Inquiries  into  Human  Faculty,  Appendix   II,  pp. 

5  Cf.  c.  y.,  R.  W.  Sellars,  Enmntitilfi  of  Loi/u-,  p.  21(5.  Ct  also  V  II 
Bradley,  Principha  of  Loijir.  p.  331,  "The  discriminative  analysis 
.  .  .  U  the  real  agent  which  .  .  .  i-ontalns  the  'Induction.' " 
\Is()  pp.  332-3.'*4,  3;i.">-33(i. 


^! 


METHODS  OF  INVESTIGATION 


203 


abstraction  and  by  determination,  and  aaaumes  some  hypoth- 
esis or  suggested  law  which  is  Intended  to  account  for  the 
concrete  situation,  and  then  proceeds  to  test  this  hypothesis 
by  the  method  of  trial  and  veriflcatlon.  The  Inductive  method 
thus  resembles  the  second  kind  of  abstraction — generalising 
or  synthetical  abstraction — except  that  Induction  sometimes 
goes  rather  beyond  the  data,  treating  them  as  a  fragment  of 
some  wider  system  than  what  is  actually  observed  in  the 
immediate  concrete  situation,  whereas  abstraction,  as  such, 
never  goes  beyond  its  data.  Induction  is  thus  a  process  which 
uses,  as  necessary  elements  in  its  construction  and  verifica- 
tion of  hypotheses,  the  two  more  general  methods  of  analysis 
and  synthesis. 

(F)  Deduction. — A  sixth  and  final  method  of  investigation 
is  deduction.  By  some  writers  deduction  is  regarded  as 
suitable  only  for  purposes  of  Exposition,  the  function  of 
Investigation  being  peculiarly  the  oflSce  of  induction.  But 
a  little  consideration  will  show  that  this  can  hardly  be  the 
case.  By  "deduction"  is  typically  understood  the  arguing 
from  a  general  principle  to  its  consequences,  and  in  almost 
all  subjects  capable  of  being  investigated  this  method  is  of 
enormous  importance.  In  fact,  the  typical  inductive  method 
is  known  as  the  "deductive  method  of  induction,"  because, 
assuming  a  hypothesis  to  account  for  our  data,  we  proceed 
to  deduce  what  would  follow  if  this  hypothesis  were  true,  and 
then  compare  our  deduced  consequences  with  what  we  find 
empirically  to  be  the  case.  A  ntudent  who  can  reason  deduc- 
tively— i.  e.,  can  draw  conclusions  from  premises  and  see  Into 
what  consequences  the  adoption  of  a  principle  will  lead  him 
— can  usually  see  his  way  into  a  problem  better  than  a  student 
who  has  not  mastered  this  method.  The  importance  of  such 
methodical  insight  for  solvin^;  problems  is  obvious,  and  we 
shall  accordingly  regard  deduction  as  a  method  of  investiga- 
tion. Like  induction,  it  is  not  independent  of  analysis  and 
synthesis — in  fact  certain  modern  logicians  tend  to  distin- 
guish an  analytical  form  from  a  synthetical  form  of  deduc- 
tion, as  methods  appropriate  to  different  classes  of  problems. 

Summary. — Analysis,  then  and  synthesis,  abstraction  and 
determination,  induction  and  deduction,  are  the  most  generally 
recognised  meth<)ds  of  scientific  investigation.  The  most  wide- 
reaching  and  the  most  universally  present,  are  analysis  and 
synthesis,  but  in  solving  any  complex  problem,  in  life  or  In 


n:i 


204    CHARACTKRISTICS  OF  SCIENTIFIC  METHOD 


hi  ! 
If  > 
I 


r 


,iij 


science.  It  is  usual  to  employ  every  one  of  these  methods. 
Definition  and  the  concept,  classiflcatlon  and  the  organisation 
of  systems,  are  also  pressed  into  the  service  of  investigation. 
But  these  subjects  are  usually  treated  under  the  head  of  Expo- 
sition, to  which  we  next  turn. 

Forms  of  Systematic  Exposition.— Exposition  cannot  be 
sharply  distinguished  from  Investigation.  In  scientific  prac- 
tise, there  Is  no  form  of  Exposition  which  Is  not  frequently 
used  In  Investigating  new  problems,  and  there  Is  no  method 
of  Investigation  which  cannot  be  used  In  systematising  one's 
conclusions  or  In  explaining  them  to  others.  In  fact,  some 
of  the  best  expositions  are  deliberate  repetitions  of  the 
methods  by  which  scientific  problems  are  investigated.  The 
laboratory  method  of  studying  known  scientific  laws  is  of 
this  kind,  and  so  Is  the  attempt  to  understand  ethical  prob- 
lems by  the  "case-method,"«  or  the  study  of  a  poem  like 
Kubla  Khan,  or  a  book  like  the  Critique  of  Pure  Reason  by 
following  the  Werdegang,  the  processes  through  which  the 
author  passed  In  coming  to  write  it. 

But  in  spite  of  this  confusion  of  methods  In  practise,  a  gen- 
eral distinction  of  purpose  can  be,  and  in  a  discussion  of 
logical  theory  should  be,  clearly  established.  In  Investiga- 
tion, our  primary  Interest  lies  In  the  direction  of  making  dis- 
coveries and  reaching  Important  conclusions.  In  Exposition, 
we  are  interested  primarily  in  stating  those  conclusions 
clearly  and  in  systematic  connection  with  other  conclusions 
or  with  general  knowledge,  and  especially  in  proving  to  others, 
as  well  as  to  ourselves,  that  our  investigations  have  actually 
succeeded  In  establishing  some  principle  or  In  solving  some 
problem.  Proof  and  the  organisation  of  what  we  already 
know  are  thus  the  main  goals  of  Exposition,  though  in  attain- 
ing these  ultimate  alms  there  are  also  certain  simpler  forms 
which  must  first  be  considered. 

(A)  Definition.— The  very  first  of  all,  a  form  of  exposition 
presupposed  by  all  organisation  of  knowledge  for  purposes 
of  either  explanation  or  proof,  is  definition.  In  the  very 
beginnings  of  an  enquiry  or  of  an  explanation.  It  is  advisable 
to  lay  down  and  determine  certain  lines  along  which  the 
enquiry  or  explanation  is  to  proceed.     This  is  the  function 


0  Cf.  O.  C.  Cox,  The  Tase  Method  In  Kthics,  Journal  of  Philoaophu 
Psycholoj/y  and  SrUntiftr  Mdhodn,  Vol.  XI,  1914,  pp.  16-23.  Cf.  Vol 
XIII,  1916,  pp.  212-213. 


FORMS  OF  EXPOSITION 


205 


of  a  preliminary  definition.    In  fact,  definition  meant,  draw- 
ing the  lines  wblch  separate  one  direction  of  thought  from 
another,  delimiting  a  field  of  enquiry  or  explanation,  itating 
what  an  object  is  In  euch  a  way  that  we  can  place  it  roughly 
within  a  system  of  problems  or  within  some  special  depart^ 
ment  of  knowledge.     This  latter  portion  of  the  meaning  of 
definition  is  exemplified  especially  at  the  end  of  an  enquiry 
or  explanation,  when  we  conclude  with  a  clear-cut  and  more 
final  idea  of  the  object  studied.    Such  a  result  of  final  defini- 
tion is  known  as  a  concept.    Definition,  then,  has  a  place  both 
at  the  beginning  and  at  the  end  of  a  process  of  enquiry  or 
explanation.      A    preliminary   definition   tends   to   emphasise 
rather    the    elements    which    together    make    up    the    object 
studied,   and   the   concluding  definition   tends  to  emphasise 
rather    the    principle   of   construction,    in    accordance    with 
which  the  elements  can  be  put  together.     In  any  case,  how- 
ever, the  function  of  definition  is  fundamental  in  exposition. 
In  order  tc  classify,  we  must  know  definitely  what  the  ele- 
ments to  be  classified  are — i.  c,  we  presuppose  that  they  are 
defined.    So  too  In  order  to  prove  any  proposition,  we  must 
know  definitely  what  we  wish  to  prove  and  what  elements 
play  a  part  in  the  argument — that  is  to  say,  proof  also  pre- 
supposes definition.     In  general,  then,  definition  is  a  form  of 
exposition  which  we  must  regard  as  fundamental,  as  a  neces- 
sary pre-requisite  of  all  the  more  complex  forms  of  exposition. 
(B)   Classification. — A  second  form  of  exposition  which  ia 
closely  connected  with  definition  is  classification.    In  investi- 
gating or  in  expounding,  we  find  it  helpful  to  group  together 
a  r  umber  of  kindred  elements  so  as  to  form  a  single  group 
or  .^lass.     When  we  can  place  some  object  of  study  in  its 
proper  context,  when  we  can  assign  it  to  some  class  of  which 
something  is  already  known,  we  at  once  feel  that  we  know  a 
great  deal  about  that  object.    If  we  know  that  a  Mr.  Smith  is 
to  deliver  a  public  lecture,  we  do  not  feel  more  than  mildly 
interested.    He  is  only  "a  Mr.  Smith"  to  us.    But  if  we  learn 
that  he  is  a  distinguished  author,  and  a  prominent  Democrat 
or  Republican,  we  at  once  know  much  more  about  him.    If 
we  learn  further  that  he  is  an  ofllcial  representative  of  a 
certain  group  of  interests,  and  that  he  is  to  speak  on  behalf 
of  these  interests,  his  meaning  and  value  for  us  as  an  author- 
ity on  h;s  subject  are  increased,  and  we  may  go  and  listen 
to  his  address.     In  this  way.  then,  we  classify  or  arrange 


11 


206    CHARACTERISTICS  OF  SCIENTIFIC  METHOD 

objects  In  groupa.  because  they  thui  throw  light  upon  one 
another,  whether  for  puf:)o»eB  of  Investigation  or  for  pur- 
poses of  expoBltion.  We  And  that  to  put  together  objects 
which  logically  belong  together— i.  ♦•..  objects  which  belong  to 
the  same  unlviTKe  of  dlscourHe,  or  have  kindred  meuflngs— 
is  a  great  help  both  1     acquiring  and  In  transmitting  knowl 

edge. 

(C)  Proof— A  third  form  of  systemhtlc  expoBltlon  Is  proof. 
To  prove,  whether  to  ourselves  or  to  others,  Is  so  Important 
a  part  of  logic,  that  some  of  the  older  text  books  did  not  hesi- 
tate to  define  their  study  as  the  "science  of  Inference  and 
proof."     In   a   sense,   every    method    of   Investigation    which 
reaches  a  valid  conclusion  Is  a  kind  of  proof,  and  It  is  some- 
times stated  that  In  Euclidean  geometry  the  genuine  proof  la 
already  given   In  the  construction.      But    the    formal    proof 
which   justifies   the   construction   to   others— or  to   oneself— 
usually  follows  other  paths,  and  tends  to  consist  In  showing 
that  what  seems  strange  or  novel  about  the  theorem  In  ques- 
tion   really    follows   from,   or   Is   logically    of   a   piece   with 
theorems  or  propositions  previously  understood  and  accepted 
as  valid.     If  direct  Insight  has  not  been  attained,  a  form  of 
argument  known  as  indirect  proof  is  sometimes  used.    This 
resembles  the  reductio  ad  absurdum  arguments.     We  show 
that  the  opposite  of  the  proposition  which  we  wish  to  prove 
leads  to  conclusions  which  do  not  fit  In  with  what  we  already 
believe  on  the  subject  in  question,  as  Herbert  Spencer  seeks 
to  prove  that  pleasure  la  an  Important  ethical  good  by  show- 
ing that  Its  opposite,  pain.  Is  universally  regarded  as  an  evil, 
and  that  to  suggest  that  we  should  seriously  pursue  pain  Is 
Inconsistent  with  all  that  we  believe  of  human  mot'ves.T    indi- 
rect proof  Is  seldom  as  satisfactory  as  direct  proof,  but  there 
are  almost  always  many  lines  along  which  we  can  advance  to 
a  definite   proof,  and  sometimes  methods  which  seem  more 
roundabout  and  Indirect  are  found  more  satisfactory  and  con- 
vincing In  the  end.     This  Is  the  case  especially  where  some 
science  Is  still  in  Its  earlier  stages,  and  Insight  Into  Its  sub- 
ject-matter  Is  still  largely  to  seek.    .Needless  to  say,  proof 
uses  all  the  methods  of  analysis  and  synthesis  already  con- 
sidered, and  may  be  either  deductive  or  Inductive,  according 
to  circumstances. 

TB*e  Spencer's  Data  of  Bthict.  chapter  111.  esp.  p.  22.  8pencer|« 
test^  t^rtnith  'Nf  any  proposition  Is  known  as  "the  InooncelyabUlty 
of  the  opposite." 


;i ,» 


/A/V-« 


FORMS  OF  EXPOSITION 


•'k^' 


^ 


207 


(D)  tysttm  of  the  Selcnett.— These  three,  then—deflnition. 
clasaiflcatioD,  and  proof— are  the  chief  forme  of  syatematic 
expoflition.  It  is  usual,  however,  to  add  to  a  study  of  theee 
forms  acme  consideration  of  the  ideal  towards  which  exposi- 
tion tends — viz.,  the  natural  system  of  the  sciences— ad  a  con- 
crete account  of  the  Icind  of  knowledge  at  which  scientific 
method,  in  the  forms  of  Investigation  and  exposition,  aimi — 
the  itnowlcdge  which  in  its  applied  forms  aims  at  enriching 
our  practical  life  with  all  the  resources  which  intellect  can 
muster  for  the  service  of  society. 

Summary.- The  general  characteristics  of  scientific  method, 
then,  vary  according  as  the  aim  Is  Investigation  or  exposi- 
tion. The  methods  of  Investigation  are  analysis  and  synthe- 
sis, abstraction  and  determination,  induction  and  deduction. 
The  chief  forms  of  systematic  exposition  are  definition,  classi- 
fication, proof,  and  the  system  of  the  sciences.  It  remains  toP 
study  each  one  of  these  general  characteristics  of  scientific; 
method.  In  the  chapters  which  follow. 

FOR  FURTHER   READING 
W.  Wttndt,  Louik,  (3rd  VA\t.),  Vol.  II,  pp.  1-2,  38-40. 

BXERCI8BS 

1.  What  are  the  chief  dilferencea  between  sclenilflc  and  unaclentlfli. 
method  In  the  following  cases :  (a)  In  purchaalng  household  furni- 
ture, (b)  In  receiving  and  answering  letters,  (c)  In  studying  a 
foreign  language? 

2.  Show  how  analysis,  abstraction,  ac".  the  other  methods  of 
Investigation  might  be  applied  In  the  following  cases :  (a)  In  choos- 
ing a  career,  (b)  In  estimating  and  judging  character,  (c)  In 
research  work  (In  a  laboratory  science,  or  In  a  literary  or  historical 
science). 

3.  Show  how  definition,  classification,  and  proof  could  be  used 
In  the  following  cases:  (a)  In  writing  «n  fssay  on  the  value  of 
travel  In  broadening  the  mind,  or  on  the  unaccountablllty  of  tastes, 
(b)  In  teaching  elementary  alf^ebra  or  geometry  to  a  high  school 
class,  (c)  In  explaining  to  a  friend  how  to  repair  a  minor  Injury 
to  his  automobile,  or  how  to  study  efficiently  for  examlna.tlona. 


V  .'^  ♦' 


CHAPTER  XIX 


ANALYSIS 


111 


Divide  et  impera  is  the  motto  of  analysis.  '  music  student 
who  wishes  to  master  the  difficulties  of  somt  ;tudy  does  no: 
practise  the  stn-^y  as  a  whole,  but  splits  It  u;  into  subjects 
or  even  phrases  and  practises  these,  one  by  one,  first  with  the 
right  hand  alone,  then  with  the  left  hand  alone,  and  finally 
with  boih  hands  together,  paying  the  utmost  attention  to 
every  detail.  So  too  a  recruit  learning  the  manual  of  arms 
divides  the  more  complex  movements  into  a  number  of  ele- 
mentary unit-mo-"ements,  and  practises  every  detail  of  these 
movements  separately  in  order  to  present  a  good  appear- 
ance at  drill.  So  also  in  carrying  through  a  naMon-wide  cam- 
paign, whether  for  political,  economic,  or  religious  purposes, 
the  country  is  divided  into  a  number  of  divisions,  each  of 
these  divisions  into  districts,  each  of  these  districts  into  sub- 
districts,  until  finally  the  whole  territory  is  parcelled  out  In 
such  a  way  that  one  or  two  campaigners  are  responsible  for 
each  block  or  ward.  In  short,  whether  the  aim  is  success 
In  winning  battles,  or  success  in  any  other  large  and  complex 
purpose,    analysis    is    the    first   and    most   universal   method 

adopted. 

Nature  of  Analysis.— What  exactly  is  analysis?  Perhaps 
we  can  obtain  the  best  mental  picture  o.'  what  is  meant  in  the 
following  way.  Imagine  a  bundle  of  sticks,  fastened  together 
by  a  rope.  If  we  untie  the  rope,  the  bundle  falls  apart  Into 
Its  constituent  elements— the  sticks.  An.ilysls  means  pre- 
cisely that— untieing  or  loosening  up— and  no  more.  Analysis, 
as  such,  introduces  no  new  purposes,  and  is  concerned  with 
no  ulterior  motives.  It  simply  looses  the  bonds  of  connec- 
tion and  lets  the  material  thus  set  free  from  what  held  it 
together  fall  apart  as  It  will,  whatever  elements  happen  to 
be  there.  It  is  absolutely  vital  to  the  method  as  scientific 
that  this  should  be  so— that  the  material  should  be  permitted 
to  fall  apart  in  its  own  way,  into  its  own  elements,  and 
that  there  should  be  no  interference  in  the  way  of  suppression 

208 


titi 


NATURE  OF  ANALYST' 


209 


or  addition,  no  re-arrangement,  no  selection  or  introduction 
of  a  prejudiced  or  arbitrary  viewpoint.  The  sole  aim  of 
analysis  is  vliat  the  connection  should  be  loosed  and  the 
material  fall  apart  Into  its  constituent  elements.  The  bundle 
must  cease  to  exist  as  a  bundle.  We  must  have  in  its  place 
a  number  of  sticks  and  a  piece  of  rope — preferably  without 
the  slightest  suggestion  of  their  ever  having  formed  a  bundle 
or  being  usable  in  any  special  way,  in  order  that  the  subse- 
quent examination  may  be  absolutely  free  from  subjective 
coloring  or  prejudif^e,  and  can  proceed  to  deal  with  the 
objects  objectively. 

The  Aim  of  Analysis. — There  is  thus  an  aspect  of  will,  pur- 
pose, or  design,  in  analysis.  We  intend  in  the  first  place  that 
the  material  shall  actually  fall  apart,  and  shall  fall  apart 
into  elements  or  units,  portions  which  can  be  regarded  as — 
at  least  for  owr  purposes — ultimate.  We  intend,  that  is,  that 
the  analysis  shall  not  in  any  way  fail,  but  shall  be  carried 
right  through  to  its  logical  conclusion.  Analysis  is  to  be  com- 
plete. There  must  be  no  residuum  which  obstinately  defies 
our  efforts  at  analysis,  but  the  whole  must  be  taken  apart 
without  remainder.  In  the  second  place,  we  intend  that  the 
material  shall  fall  apart  into  elements  which  are  its  own,  that 
the  bond  of  connection  which  we  loose  shall  really  be  the 
bond  which  in  fact  holds  together  the  elements  in  question. 
We  intend  to  follow  natural  lines  of  cleavage,  to  divide  up 
the  object  In  accordance  with  its  own  nature.  It's  own  law 
of  connection.  Analysis  Is  to  be  objective.  We  intend  that 
analysis  shall  not  fail  by  containing  elements  which  are  ficti- 
tious, mental  fictions,  fanciful,  arbitrary,  subjective,  but  that 
it  shall  cross  the  line  which  divides  the  fictitious  from  real, 
the  subjective  from  the  objective,  and  shall  deal  with  the 
actual  nature  of  the  actual  object.  Completeness  and  objec- 
tivity— these  represent  the  aim  of  analysis. 

How  far  Realisable?  (A)  In  Man-Made  Structurr'  •  \d 
Mental  Models. — How  far  can  this  aim  be  realised?  tts 

consider.  A  recruit  is  shown  how  to  take  his  rifie  to  pieces. 
By  turning  here  and  pulling  there  he  can  take  It  to  pieces 
In  a  way  which  is  objective — for  the  striker,  follower,  main 
spring,  etc.,  are  actual  parts  of  the  actual  rifle.  But  hto 
analysis  is  not  coaiplete.  By  the  use  of  a  screw-driver,  the 
armorer  will  take  the  rifle  still  further  apart,  until  he  ham 
reduced  it  to  its  last  elements.    His  aDalysis  is  both  objee- 


210 


ANALYSIS 


tive  and  complete.  So  too,  th^  use  of  a  screwdriver  and  a 
wrench,  plus  the  methods  of  pulling,  pushing,  and  turning, 
will  suffice  to  take  to  pieces  a  type-writer  or  piano,  complex 
though  these  objects  are,  and  such  a  analysis  can  be  not 
only  objective,  but  also  as  complete  as  we  please.  In  fact, 
any  machinery  which  the  mind  of  man  can  devise,  the  mind 
of  man  can  also  take  to  pieces.  Artefacts,  then,  i.  e.,  man- 
made  objects  fashioned  in  accordance  with  some  rational  plan, 
can  be  analysed  in  a  way  which  Is  both  objective  and  com- 
plete. . 

Let  us  consider  another  class  of  cases.     A  complex  arltn- 
metlcal  example  can  be  reduced  to  a  number  of  simple  opera- 
tions with  units.    A  complex  geometrical  figure  can  be  reduced 
to  a  combination  of  simple  lines  and  points.    And  generally 
speaking,  mathematics  presents  us  with  a  host  of  complexes 
which  the  mind  of  man  can  take  apart  because  the  mind  of 
man  has  put  them  together,  and  put  them  together  in  accord- 
dance  with  a  rational  plan,— a  plan  which  the  mind  of  man 
can  understand.    These  cases  are,  in  fact,  typical  of  the  vast 
number  of  thought-structures  to  which  we  have  referred  as 
mental  models.     Whatever  reason  has  constructed  In  accor- 
dance with  its  own  laws,  reason  can  take  to  pieces  again  In 
a  way  which  is  both  objective  and  complete.    Whatever  has 
been  constructed  in  accordance  with  intellectual  standards  or 
Intellectual   demands,   can  be   analysed   in   accordance   with 
intellectual   demands,   and  speaking  generally   we  can   say: 
Whatever  is  rational  can  be  analysed,  and  can  be  analysed 
just  so  far  as  It  is  rational,  whether  it  Is  a  mathematical 
problem,  a  carefully  thought-out  plan  of  life,  an  esthetlcpl 
composition,  or  a  piece  of  mere  machinery.    In  such  cases, 
where  thought  apprehends  the  structure  which  thought  has 
itself  introduced  In  accordance  with  Us  own  laws,  i.  e.,  where 
thought   is   dealing   ultimately   with   itself— analysis,  as   we 
have  described  It.  Is  possible.    In  such  cases  we  can  realise 
the  aim  of  objectivity  and  completeness. 

It  remains  to  consider  a  further  point.  Whatever  Is  rational 
can  theoreticallv  be  analysed.  But  In  order  that  this  theoret- 
ical possibility  should  be  realised,  we  must  know  something 
more  It  Is  necessary  to  understand  the  special  law  of  con- 
nection which  binds  together  the  elements  In  question  bo  as 
to  constitute  a  rational  complex.  Without  insight  into  thl« 
law   we  cannot  know  what  are  elements  and  what  are  not. 


AIM  OF  ANALYSIS 


211 


in  a  given  case.  We  do  not  know  what  to  look  for.  Let  us 
suppose  that  we  receive  a  message  in  cipher:  "AAABBBAAB 
ABBBAAAAABBBBAAABBAABBBBAABBAAABABABIBBAA 
BBAABABAAABAAABBBAAAA."  Here  is  something  con- 
structed in  accordance  with  a  rational  plan.  But  without  the 
key,  what  can  we  do?  Suppose  we  analyse  it  Into  letters. 
That  will  not  help  us.  For  unless  the  cipher  is  constructed 
in  such  a  way  that  each  single  letter  corresponds  to  some 
single  letter  of  the  alphabet,  our  analysis  is  irrelevant.  We 
are  analysing  into  elements  which  are  not  elements  of  the 
cipher,  but  are  arbitrary.  They  are,  indeed,  in  a  sende  com- 
plete; for  nothing  is  omitted.  But  such  an  analysis  is  cer- 
tainly not  objective — i.  e.,  does  not  analyse  the  object,  the 
cipher  itself,  at  all.  As  there  are  only  two  letters,  A  and  B, 
It  is  plain  that  the  single  letter  Idea  must  be  abandoned.  We 
try  again.  Perhaps  A  represents  one  letter  of  the  alphabet, 
AA  another  letter,  AAA  yet  another,  and  so  also  with  B,  BB, 
BBB,  etc.  The  most  frequently  occurring  of  these  combina- 
tions are  AA  and  AAA.  But  here  again  we  fail,  and  our 
failure  shows  that  the  principle  in  terms  of  which  we  are 
trying  to  analyse  is  not  the  right  one.  We  try  again.  Per- 
haps some  combination  of  A's  and  B's  is  equivalent  to  each 
letter  of  the  alphabet.  We  may  remember  having  read  of 
Bacon's  bi-lit  -al  cipher,  or  we  may  t.dd  up  the  total  number 
of  letters  anu  find  that  they  will  divide  by  five,  and  thus, 
even  without  knowledge  of  Bacon,  assume  that  a  group  of 
five  letters,  consisting  only  of  A's  and  B's,  corresponds  to 
a  single  letter  of  the  alphabet.  Our  assumption  may  be  cor- 
rect, but  of  itself  does  not  suflSce  for  the  solution  of  our  prob- 
lem. We  cannot  be  sure  that  the  analysis  is  correct,  and 
that  AAABB,  BAABA,  etc.,  are  the  genuine  elements  of  the 
cipher,  until  we  have  discovered  more.  We  try  constructing 
a  cipher  in  accordance  with  the  formula  with  which  we  are 
now  experimenting.  Let  a  =  AAAAB,  b  =  AAABA,  c  = 
AABAA,  etc.  There  are,  of  course,  many  possibilities  here, 
but  we  try  the  first  one,  and  find — after  a  few  more  mistakes 
and  trials — that  it  fits.  Now  that  we  can  finally  read  off  the 
message,  and  thoroughly  understand  the  principle  of  construc- 
tion, we  can  analyse  our  problem  into  its  elements  in  a  way 
which  is  both  objective  and  complete.  What  is  neeeded  in 
order  to  realise  the  aim  of  analysis  is  (1)   that  the  object 


212 


ANALYSIS 


m 


r 


Bhould  be  constructed  in  avcordance  with  some  rational  plan, 
r  (2)  that  we  should  have  insight  into  the  plan.  Other- 
^  .e,  our  efforts  at  analysis  are  irrelevant,  and  fail  from  the 
viewpoint  of  objectivity  at  least.  Such  attempts  are  imper- 
fect and  artificial. 

(B)   In  Dealing  With  Natural  Phenomena.— Our  procedure, 
In  such  cases  as  the  above,  is  like  that  of  a  person  who  stands 
before  a  locked  door  with  a  bunch  of  keys,  one  of  which  is 
the  right  one.     He  tries  key  after  key,  until  he  comes  upon 
the  right   one.     So   too    we   tried   one   mental   model   after 
another,  until  we  hit  upon  the  one  which  exactly  fitted.    But 
we  must  now  advance  to  a  further  consideration.     In  the 
cases  hitherto  considered,  thought  is  dealing  with  its  own 
constructions,    its    own    instruments,    forged    by    itself    in 
accordance  with  its  own  laws.     In  actual  practise,  however. 
It  is  very  rarely  that  thought  either  needs  or  wishes  to  analyse 
Itself  and    its    own    constructions.      Thought-structures    are 
instruments   intended   to  solve   problems  which   face   us  In 
life— problems  in  the  objective  world,  and  in  dealing  with 
concrete  situations  it  is  a  question  whether  any  mental  model 
will  "fit"  except  very  roughly  and  approximately.     Analysis 
is  imperfect— i.  e..  we  have  to  use  models  arbitrarily  chosen, 
and  thus  not  perfectly  appropriate— (1)  when  we  do  not  know 
the  principle  which  governs  the  situation  before  us.    In  actual 
practise,  this  is  almost  always  the  case.    A  specialist  Is  asked 
to  psycho-analyse  a  hysterical  patient,  with  a  view  to  finding 
out  what  is  wrong.    No  one  knows.     He  proceeds  to  test  for 
all  the  frequent  "complexes,"  until  he  hits  upon  a  group  of 
associations  which  seems  to  be  causing  the  trouble.    This  Is  a 
lengthy  process,  and  the  preliminary  attempts  at  analysis  are 
largely  irrelevant  and.  in  some  cases,  even  misleading.    But 
further,  analysis  is  imperfect  (2)  when  our  Instruments  are 
not  perfectly  adapted  to  their  work.     The  various  diseases, 
physical  and  mental,  which  a  physician  has  to  diagnose,  are 
cases  in  point.    Every  one  knows  that  the  most  terrible  mis- 
takes sometimes  take  place.     Where  the  symptoms  are  not 
accurately  studied,  it  is  possible  for  the  physician  to  analyse 
in  terms  of  a  mental  model  which  seems  partially  to  fit  the 
case,  but  in  fact  is  tragically  beside  the  point.    Thus  typhoid 
patients  have  been  actually  treated  for  appendicitis,  cancer 
has   been    treated    as   indigestion,    and   mental   disease    has 


METHODS  OF  SCIENTIFIC  ANALYSIS 


213 


received  any  and  every  kind  of  treatment,  from  religious  ven- 
eration to  imprisonment  or  a  sound  tlirashing.i 

In  dealing,  then,  with  objects  other  than  our  own  thought- 
constructions,— that  is  to  say,  in  the  face  of  nature  with  its 
infinite  variety  of  problems — we  are  necessarily  restricted  to 
the  trial-and-error  method,  and  to  experimenting  with  ana- 
lytical models  which  we  know  to  be  more  or  less  imperfect. 
The  result  is,  that  our  conclusions  never  perfectly  apply  to 
their  material,  and  in  consequence,  our  analysis  is  hardly  ever 
complete.  There  is  almost  always  some  residuum  which  obsti- 
nately defies  further  analysis.  A  chemist,  analysing  given 
material  for  traces  of  poison,  knows  that  there  is  always  a 
certain  residuum  for  which  he  cannot  perfectly  account.  Dif- 
ferent chemists  analyse  the  same  material  but  come  to  differ- 
ent conclusions:  A  finds  5%  of  the  poison,  B  finds  6%,  and 
in  certain  cases  such  differences  are  important.  Where  our 
instruments  are  not  perfectly  adapted  to  their  material,  our 
analysis  cannot  but  be  Imperfect,  and,  as  contrasted  with  our 
perfect  success  in  dealing  with  mental  constructions,  we  can 
say  that  scientific  method,  when  applied  to  physical  or  nat- 
ural-science problems,  is  always  partly  incomplete,  and  never 
perfectly  objective.  We  deal,  not  with  things  as  they  are  in 
their  nature,  but  with  mental  models  whose  structure  we 
understand,  and  the  difference  between  the  mental  model  and 
the  actual  given  situation  is  the  unanalysed  residuum  which 
is  the  measure  of  our  practical  success  or  failure.  If  the  dif- 
ference is  large,  we  fail.  If  it  is  negllglWe,  we  succeed  In  prac- 
tise. But  a  theoretically  perfect  analysis  of  natural  phe- 
nomena is  an  unattainable  ideal. 

METHODS   OF   SCIENTIFIC    ANALYSIS 

(A)  Mathematical. — But  because  our  efforts  at  analye's  are 
empirical  and  imperfect.  It  does  not  follow  that  we  cannot  at 
least  approximate  to  results  which  we  can  accept  as  satisfac- 
tory. Even  mistaken  experiments  succeed,  as  a  rule,  in  assist- 
ing us  to  some  Insight  into  the  problem  studied.  In  the  case 
of  the  cipher,  which  we  analysed  above,  we  gradually  worked 
our  way  to  a  method  which  was  satisfactory.  So  also  in  nat- 
ural science.    We  almost  always  begin  with  some  method  of 

1  Cf.  B«maTd  Haxt,  Ptychology  of  In$anity,  ch&pter  1. 


214 


ANALYSIS 


lifj 

.i  ■ 

r 

■i    : 
•  i    I 

11 


ttit 


analysis  which  we  Itnow  to  be  merely   preliminary,  because 
experience  shows  that  It  is  helpful  in  preparing  the  material 
for  a  more  final  kind  of  analysis,  and  in  giving  us  a  kind  of 
Insight   which,   without  such   preliminary  analysis,   we  lack. 
Thus,  in  attacking  many  a  psychological  or  sociological  prob- 
lem, while  we  know  that  the  only  kind  of  analysis  which  can 
yield  us  final  satisfaction  will  be  specifically  psychological  or 
sociological,  we  be?ln  with  an  analysis  which  Is  mathematical. 
In  all  the  natural  sciences,  mathematical  analysis  la  an  aux- 
iliary method  of  the  greatest  Import.  ..ce.     So  far  as  it  goes, 
It  Is  sufficiently  exact,  and  It  tends  to  leave  the  material  in 
better  shape  for  a  more  final  analysis.  For  Instance,  how  long 
should  a  Dachshund  of  given  girth,  head,  and  tail,  be  in  the 
body  in  order  to  give  the  most  esthetical  satisfaction?     For 
experimental  purposes,  a  model  Dachshund  is  used,  made  of 
celluloid,  the  body  of  which  can  be  elongated  or  contracted  by 
means  of  an  apparatus  which  admits  of  exact  measurement  In 
terms  of  a  millimeter  scale.    Starting  with  a  short  Dachshund, 
we  observe  it  as  it  is  gradually  lengthened,  until  we  feel  that 
it  is  just  right.    A  record  is  taken  of  the  measurement,  and 
we  try  again.    After  many  such  attempts,  we  commence  with  a 
Dachshund  which  Is  much  too  long,  observe  it  as 'it  grows 
shorter,  until  we  feel  that  it  is  just  right.    Finally,  the  aver- 
ages of  the  various  measurements  are  taken,  and,  after  a  num- 
ber of  mathematical  manipulations  of  the  mathematical  data, 
we   reach   certain   conclusions   as   to   the   variability   of   the 
esthetical  judgment,  £tnd  also  as  to  certain  of  the  conditions 
which  infiuence  it.     Such  an  analysis  does  not  take  us  very 
far,  and   experimental  esthetics  generally  Is  still   In  a  very 
preliminary  stage,  but  still,  a  beginning  has  been  made,  and 
has  been  made  by  using  methods  which  are,  at  least  in  part, 

mathematical. 

So  too  with  problems  which  are  sociological.  Is  there  really 
any  definite  connection  between  drink  and  crime?  Is  imbe- 
cility hereditary?  What  factors  govern  the  increase  or 
decrease  of  population?  In  studying  such  problems,  mathe- 
matical analysis  is  vital.  Without  statistical  methods  of  con- 
siderable refinement,  the  material  could  never  be  reduced  to 
a  form  which  the  scientist  could  use.  This  is  true  also  of 
Intelligence  tests,  tests  of  bodily  efficiency,  and  generally,  in 
all  cases  which  admit  of  the  application  of  mathematical 
methods  of  analysis.    Breaking  up  a  vast  and  complex  situa- 


METHODS  OF  SCIENTIFIC  ANALYSIS 


215 


tlon  Into  elements  which  can  be  counted  and  shifted  around 
In  accordance  with  quantitative  methods  is  almost  always 
helpful  In  adding  to  our  Insight  Into  the  structure  of  a  con- 
crete problem.2 

(B)  CauMl. — A  second  mental  model  which  experience  simi- 
larly shows  to  be  helpful  In  approaching  the  analysis  of  a  con- 
crete situation  Is  the  cause-and-effect  principle.    This  Is  found 
helpful  in  analysing  processes,  events,  and  generally  any  phe- 
nomena which  occupy  time.     Mathematical  models  are  also 
employed  as  a  rule,  because  of  their  value  as  auxiliary  meth- 
ods.    But  In  dealing  with  processes  and  events,  we  tend  to 
split  the  phenomena  up  into  groups  which  are  not  so  much 
1»  2.  3,    .    .    .    ,  as  before-and -after  groups,  antecedents  and 
consequents,  cause-and-effect  groups.    The  physician  called  In 
to  diagnose  a  case  begins,  It  Is  true,  by  listing  the  symptoms. 
But  his  analysis  throughout  has  less  of  mathematical,  and 
more  of  causal  reference.    The  enumeration  of  symptoms  Is 
less   Important   as   enumeration — i.    e.,   mathematically— and 
more  Important  as  throwing  light  upon  causes,  as  a  sore  throat 
followed  at  a  certain  interval  by  a  rash  implies  scarlet  fever 
or  measles,   or   as  certain   disturbances  of  digestion   Imply 
decayed  teeth,  etc.     So  too  a  professional  man,  In  analysing 
the  noises  which  disturb  him  at  his  work,  is  not  content  with 
a  mere  enumeration,  but  analyses  with  a  very  definite  causal 
reference.     Thus,  freight-train  disturbances  point  to  Increas- 
ing   traffic,    and    thus    to    prosperity;    passing    automobiles, 
whether  for  business  or  pleasure,  seem  to  point  In  the  same 
direction;   while  certain  other  noises  point  to  causes  which 
should,  in  his  opinion,  be  eliminated.     In  fact,  during  the 
greater  part  of  our  waking  life  we  are  analysing  with  this 
kind  of  causal  reference  all  events  which  attract  our  atten- 
tion, and  all  persons  with  whom  we  are  brought  into  con- 
tact.   On  the  whole,  then,  it  seems  legitimate  to  regard  these 
two  classes  of  mental  patterns,   the  mathematical  and  the 

T/i^=P^i^°K®  "^J^^  card-Index   methods   will  Justify   this   sutement. 
It  Is  stated  by  some  logicians  (e.  g.,  Bosanquet  and  Wundt).  that  the 
^l  2'  science  which   constitutes    Law   d^ies  not   use   mathematical 
metliods  of  analysis,  as  It   is   not   quantitative.     This  dws   not  se^ 
.♦o  be  exactly  the  case.     In  analysing  a  Concept  under  vrrlous  headaT 
'tl8,  usual    to   enumerate   the   heads   of   characteristics   1     *>    3    etr 
and  In  all  analysis   In  which  card-index  methods  nr  anvthln<'  nf  thp 
Ti,'}  ^J%^'^^l^''m?'  U'^re '8  *  tendency  to  treat  each  record  as  a  "unit," 
?S?«?J''lK?'i®'"^''**"'*  regroupings  of  these  records,  certain  mcth<^ 
are  tised  which  are.  to  some  extent  at  least,  mathematical.     It  is  true 
^"T^IS'''  *,^**  '"  t5*°^J.  i"^  practise  of  Jurisprudence,  mathematlca 
methods  play  a  part  which  Is  at  best  only  subordinate       """"'^"""'^a' 


?16 


ANALYSIS 


causal,  as  the  most  universal  and  the  most  helpful  of  all  our 
preliminary  and  Imperfect  methods  of  scientific  analysis. 

Validity  of  Methods  of  Scientific  Analysis.— The  mental  pat- 
terns employed  in  scientific  analysis,  as  exemplified  in  quan- 
titative and  causal  explanations,  are  in  part  inadequate.  But 
on  the  wbol  ,  they  are  /ound  helpful  in  giving  us  Insight  into 
the  structure  of  natural  phenonena.  On  what  does  this  help- 
fulness depend,  and  how  far  can  we  feel  justified  in  approach- 
ing nature  in  the  attitude  of  a  Judge,  and  compelling  her  to 
answer  our  carefully  prepared  questions?  To  this  query,  there 
is  only  one  answer  which  we  can  regard  as  admissible.  Our 
analytical  methods  are  justified  only  so  far  as  they  are  found 
intelligible  on  the  one  hand,  and  found  to  "work"  on  the 
other.  They  should  not  only  be  intelligible  in  themselves,  and 
form  part  of  a  consistent  system  of  similar  mental  models,  but 
should  also  be  justified  in  terms  of  sensory  experience.3  They 
should  approximate  to  the  completeness  and  objectivity  which 
are  such  conspicuous  features  of  our  analysis  when  thought 
examines  only  its  own  constructions.  So  far  as  our  empirical 
analyses  fall  short  of  these  standards  of  completeness  and 
objectivity,  so  far  these  serve  as  encouragements  to  pursue  and 
follow  our  path  yet  further,  and  it  is  only  by  continued  and 
unwearied  experimentation  that  we  come  to  adjust  our  mental 
models  more  closely  to  the  empirical  facts,  and  thus  approxi- 
mate more  and  more  to  a  validity  which,  in  dealing  with  nat- 
ural phenomena,  appears  to  be  beyond  our  reach. 

Summary. — So  far  then,  we  have  seen  that  analysis  is  a 
preliminary  portion  of  scientific  method,  and  that  its  appli- 
cation is  universal.  Its  aim  is,  to  loosen  the  bond  of  con- 
nection which  holds  a  problem  together  and  let  it  fall  apart 
into  its  elements  along  natural  lines  oi  cleavage,  in  a  way 
which  is  not  only  objective,  but  also  complete.  This  aim  can 
be  realised  in  dealing  with  mind-made  structures,  and  with 
these  only.*    In  dealing  with  natural  phenomena,  we  can  only 

3  For  an  example  of  what  to  avoid,  the  student  with  grounding  in 
psychology  Is  recommended  to  glance  over  J.  Chr.  Wolff's  Paychologia 
Fmpirica.  The  mental  patterns  are  clear  and  form  a  wonderfully  con- 
sistent group  as  a  whole,  and  yet  there  is  perhaps  not  a  single  problem 
or  theorem  In  the  whole  book  which  would  be  accepted  by  a  present- 
day  empirical  psychologist.  It  Is  weak  on  the  empirical  and  sensory 
side. 

« Machines  are  regarded,  from  a  logical  viewpoint,  as  mind-made 
structures.  It  is  only  fc  >  far  as  they  are  made  strictly  In  accordance 
with  our  mental  patterns  that  we  fully  understand  them.  Cf.  Bosaa- 
quet,  £<8ential»  of  Logic,  p.  12P,  who  treats  a  portion  of  a  railway 
track  as  a  materialised  disjunctive  judgment. 


EXERCISES 


217 


approximate  to  an  accurate  analysis  by  experimenting,  and 
trying  whether  this  mental  model  or  that  will  apply.  The 
most  universally  usable  and  the  most  generally  helpful  of 
such  mental  patterns  are  the  mathematical  and  the  cause-and- 
effect  models.  Though  not  perfectly  satisfactory,  they  can 
still  be  accepted  as  trustworthy  so  far  as  they  are  found  to 
"work,"  and  to  bring  us  into  closer  touch  with,  and  under- 
standing of,  concrete  problems.  By  such  means  we  can  hope 
for  a  gradually  increasing  insight  into  the  structure  of  phys- 
ical phenomena,  and,  indeed  of  all  phenomena  whatever  which 
can  be  analysed  in  this  way. 


FOR  FURTHER   READING 
W.  Wundf.  Logik.  (3rd  VA\t.),  Vol.  11,  pp.  2-8. 

EXERCISES 

Show  what  part  is  played  by  analysis  In  dealing  with  the  following 
cases:  (1)  In  learning  to  play  tennis  or  golf.  (2)  In  nukklng  one- 
self popular.  (3)  In  finding  out  what  is  wrong  with  an  automobile 
which  suddenly  refuses  to  work.  (4)  In  finding  one's  way  about  a 
new  city.  (5)  In  looking  up  facts  or  dates  in  the  encyclopedia.  (6) 
In  securing  a  position. 


I! 


CHAPTER  XX 

SYNTHESIS 

"Putting  two  and  two  together"  is  one  of  the  most  Impor- 
tant of  all  our  intellectual  activities.  Without  this  function, 
we  should  be  imbeciles,  unable  to  hold  more  than  a  single 
Idea  in  our  minds  at  a  time  and  Incapable  of  performing  the 
slightest  service  for  others,  or  even  for  ourselves.  With  it. 
we  have  an  instrument  which  is  indispensable  in  every  walk 
of  life.  By  its  aid  we  construct  our  daily  plans,  our  science, 
our  art,  and  our  religion.  Our  whole  political  and  economic 
life  rests  upon  it,  and  so  vital  does  it  appear  in  our  reasoning 
processes,  that  philosophers  like  Aristotle  and  Kant  have 
regarded  synthesis  as  the  most  characteristic  function  of 
mind,  and  psychologists  like  Binet  and  Yerkes  rank  synthetic 
ability  as  evidence  of  advanced  Intelligence.! 

Nature  of  Synthesis.— What  precisely  do  we  understand  by 
"synthesis"?  It  Is  the  opposite  of  analysis.  Analysis  takes 
apart.  Synthesis  puts  together.  Given  a  concrete  situation, 
analysis  reduces  It  to  separate  elements.  Given  separate 
elements,  synthesis  reduces  them  to— what?  Let  us  consider. 
Defends,  a.  his,  dog,  master,  good,  bravely.  Here  we  have 
a  number  of  separate  elements.  Synthesis  puts  them  together 
In  such  a  way  that  they  make  sense— i.  e.,  in  such  a  way 
that  they  express  a  certain  unity  of  meaning.  "Two  N's, 
two  O'a  an  L  and  a  D,"  says  the  child,  "Put  them  together 
and  spell  them  to  me."  Here  again,  it  is  a  question  of  putting 
them  together  so  that  they  form  a  rational  unity.  Analysis, 
we  remember,  meant,  not  merely  taking  apart,  but  loosening 
a  bond  of  connection,  the  principle  which  held  together  the 
phenomenon  studied.  Synthesis,  then,  means,  not  merely 
putting  together,  but  introducing  some  unifying  plan,  some 
rational  principle  of  connection,  so  that  In  place  of  a  mere 
aggregate  or  disconnected  heap  we  have  a  genuine  totality. 


AMUti/.YQli^'^"^^^^'^^''^^^'^^'  "*  ^<'*«*-'SfcaIe  for  Meaturing  Mental 


i-, 

■  .f  ■ 


218 


AIM  OF  SYNTHESIS 


219 


an  organised  whole  composed  of  elements  which  ara  united 
— i.  e.,  belong  together  and  conatitute  a  single  entity,  an 
individual. 

Aim  of  Synthesis  (A)  Objectivity— Synthesis  means,  then, 
no  merely  mechanical  juxtaposition,  but  p  putting  together 
which  really  puts  d  ther,  so  that  the  elements  which  are 
syntheslsed  enjoy  a  genuine  togetherness,  and  constitute  a 
unity  which  is  rational.  It  means  Intelligent  construction, 
rational  organisation,  and  involves  the  application  of  intel- 
lectual principles  to  elementary  data.  Synthesis  aims,  then, 
at  organiaatinn  of  the  data,  and  at  an  organisation  which  la 
rational.  It  also  aims  at  organisation  of  the  data.  That  la 
to  say,  like  analysis,  it  alms  at  objectivity.  Xo  rational 
person  would  attempt  to  construct  a  triangle  out  cf  tones 
or  a  melody  out  of  straight  lines.  In  every  case  the  principle 
of  unity  which  synthesis  Introduces  must  unify  the  elements 
with  which  we  start,  and  must  bind  them  together  In  a  way 
which  Is  suited  to  their  nature.  Otherwise  we  fail  in  respect 
of  objectivity. 

(B)  Completeness.— Can  we  say  that,  lilte  analysis,  syn- 
thesis also  alms  at  completeness?  Let  us  consider.  At  a 
rational  completeness  It  certainly  does  aim.  For  this  Is 
involved  in  the  very  notion  of  objectivity.  Thus,  given  the 
barrel,  stock,  magazine,  cocklng-piece,  etc., — i.  e.,  the  ele- 
ments out  of  which  a  Springfield  rifle  is  constructed— there 
is  only  one  rational  way  of  assembling  the  parts.  If  they  are 
to  form  the  unity  for  which  they  are  adapted,  it  will  be  neces- 
sary to  omit  nothing,  but  to  include  every  single  element. 
So  too,  given  the  requisite  number  of  automobile  parts,  there 
is  only  one  way  in  which  these  also  can  be  assembled  so  as 
to  constitute  a  genuine  unity— the  unity  for  which  they  are 
objectively  adapted.  No  single  part  can  be  omitted.  The 
synthesis  must  be  complete. 

That  !s  to  say,  where  the  objective  elements  are  such  as 
to  render  it  possible,  the  synthesis  should  be  complete.  But 
there  are  two  other  possibilities.  The  given  material  may 
contain  elements  which  are  too  many  or  too  few.  Out  of  an 
assortment  of  materials  taken  from  several  old  cars,  a  skilful 
mechanic  will  assemble  a  single  car  which  can  be  used.  But 
he  will  not  have  used  up  all  the  material.  It  contains  parts 
enough,  and  more  than  enough,  for  one  good  car,  but  not 
enough  for  two.     The  surplus  parts  are  thus  omitted,  and 


220 


SYNTH  KSIS 


I! 


W 


the  syntbeHia  is  not.  In  this  scnHe,  complete.  But  if  we 
underHtand  by  "conipletrneHH"  a  due  regard  for  objectivity 
and  for  what  Ih  reasonable  in  the  particular  situation,  we  can 
■ay  that  even  In  such  caHeu  our  Hynthesis  aims  ut  all  the 
completencHH  which  could  reasonably  be  demanded.  So 
again  where  the  elements  are  too  few.  In  such  caHes,  it  may 
be  impossible  to  put  them  together  objectively — e.  g.,  if  some 
vital  connecting  portion  is  missing.  Hut  in  all  such  cases 
our  aim  is  at  completeness.  Wherever  possible,  we  piece 
out  the  imperfections  of  our  material,  and  construct,  as  well 
as  we  can,  in  all  its  completeness,  the  totality,  of  which  our 
data  constitute  fragmentary  portions. 

We  may  here  note  a  certain  difference  between  analysis 
and  synthesis.  Analysis  seems  to  be  confined  exactly  to  its 
data.  Its  aim  is  thus  to  omit  no  element,  whether  relevant 
or  irrelevant,  and  to  add  nothing,  whether  some  vital  element 
has  been  omitted  or  not.  Synthesis,  on  the  contrary,  seems 
to  be  a  more  flexible  and  a  more  developed  method  than 
analysis.  It  can  omit  what  is  irrelevant  or  superfluous,  and 
can  add  what  is  missing,  or  at  least  is  Imperatively  demanded 
by  the  data  in  order  to  put  them  together.  That  is  to  say, 
synthesis  can  take  account,  to  a  greater  extent,  of  rational 
considerations,  and  is  not  so  tied  down  to  its  material.  But 
in  general  its  aim  resembles  the  aim  of  analysis,  in  that  it 
desires  above  all  things  objectivity  and  completeness. 

How  Far  Realisable?  (A)  With  Mind-Made  Entities— Give 
a  child  the  parts  of  a  jig-saw  puzzle,  or  such  letters  as 
N,  A,  T,  H,  «,  0,  O,  W,  I,  N,  and  ask  him  to  put  them 
together.  Give  an  adolescent  a  box  with  various  compart- 
ments, of  which  one  contains  the  parts  of  a  simple  bell, 
another  the  parts  of  a  simple  lock,  etc.  Within  a  reasonable 
time,  the  child  will  have  put  together  the  parts  of  the  jig-saw 
puzzle  or  the  letters  of  the  name,  and  the  adolescent  will 
show  you  a  complete  bell,  lock,  etc.  So  also  a  clock  maker 
will  assemble  the  parts  of  a  clock,  a  trained  mechanician 
will  assemble  the  parts  of  an  automobile,  etc.  In  a  word, 
wherever  we  have  the  parts  of  some  mechanism  devised  by 
the  human  mind,  the  human  mind  can  learn  to  put  those  parts 
together  iu  a  way  which  is  both  objective  and  complete.  The 
history  of  invention  further  shows  that  synthesis  can  in 
many  cases  improve  upon  the  original  principle  of  construe- 


AIM  OF  SYNTHESIS 


221 


tion,  by  deslgnlnK  models  which  use  less  material,  fewer  and 
simpler  parts,  and  In  a  word  are  more  economical  and  efBcient. 

Let  us  consider  other  cases  which  are  mind-made,  bat  less 
closely  connected  with  physical  matter.  Given  three  straicht 
lines,  of  which  any  two  are  together  greater  than  the  third. 
It  Is  possible,  upon  a  plane  surface,  to  construct  a  triangle. 
Given  the  elements  essential  for  the  solution  of  a  problem  In 
simultaneous  equations,  it  Is  possible  to  solve  that  problem. 
Given  the  concept  of  Man  as  finite.  Imperfect,  and  dependent, 
and  the  concept  of  God  with  the  traditional  attributes  of  abso- 
lute power,  absolute  knowledge,  absolute  wisdom,  etc..  It  is 
possible  to  construct  a  whole  system  of  ethics  based  upon  the 
relation  of  Man  to  God.  If  these  instances  are  typical  of 
mental  models,  we  can  state  that  whatever  elements  are 
capable  of  being  put  together  in  accordance  with  a  rational 
principle,  admit  of  a  synthesis  which  is  objective  and  com- 
plete. 

In  such  cases,  then,  it  is  theoretically  possible  to  realise 
the  aim  of  synthesis.  But  before  the  aim  can  In  fact  be 
actually  realised,  something  more  is  necessary  than  elements 
which  are  rationally  uniflable.  Take  any  college  graduate 
and  show  him  one  of  the  standard  puzzle-boxes.  Give  him 
the  following  instructions: — "Pull  out  this  lever  as  far  as 
possible.  Then  pull  out  this  second  one.  Then  stand  the 
box  upon  the  side  which  is  painted  white.  Then  turn  the 
combination  lock  twice  to  the  right,  to  the  number  47,  then 
twice  to  the  left,  to  the  number  36,  then  once  more  to  the 
right,  to  the  number  14,  and  the  door  will  open."  The  data 
here  are  the  particular  instructions,  and  the  problem  Is,  to 
put  them  together  correctly.  In  theory,  the  synthesis  can 
be  both  objective  and  complete.  In  practise,  however,  the 
average  college  graduate  will  be  unable  to  put  together  the 
elements  of  the  instructions  and  hold  them  together  In  his 
mind.  Either  he  omits  to  stand  the  box  upon  its  white  side, 
or  he  falls  to  turn  the  combination  lock  twice  to  the  left,  etc. 
That  is  to  say,  he  has  failed  to  grasp  the  rational  principle, 
in  terms  of  which  the  Instructions  form  a  unity.  In  order 
to  succeed.  It  is  essential  to  grasp  the  principle  thoroughly, 
and  to  apply  it  exactly.  So  too,  after  hearing  an  addressi  we 
find  (hat  we  can  perhaps  remember  parts  of  what  we  have 
heard,  but  that  we  cannot  put  the  parts  together  so  as  to 
form  a  rational  unity — we  have  lost  touch  with  the  principle 


222 


SYNTHESIS 


T{ 


I 


■  i  ii  ■ 


pi 

in 

ir 


which  made  the  connection  and  sequence  of  thoughts  clear. 
So  too  in  carrying  through  our  life-plans,  there  are  times 
when  we  lose  sight  of  our  guiding  principles.  In  such  cases 
we  find  ourselves  unable  to  make  sense  of  our  experience, 
and  we  blunder  along  at  haphazard.  In  order,  then,  that  the 
aim  of  synthesis  may  be  realised,  it  is  necessary,  not  only 
(1)  that  the  data  shall  be  rationally  uniflable,  but  also  (2) 
that  we  thoroughly  understand  the  rational  principle  which 
is  the  key  to  their  synthesis  in  practise.  Then,  and  then 
only,  can  we  advance  to  a  synthesis  which  shall  be  both 
objective  and  complete. 

Just  what  is  our  procedure  when  we  are  without  insight 
into  the  principle  of  connection?  Let  us  consider  an  instance. 
Hour,  for,  we,  early,  at,  park,  an,  started,  the,  of,  morning. 
Here  we  have  a  number  of  elements  which  can  be  put  together 
so  as  to  make  sense.  How  do  we  synthesise  them?  We  read 
over  the  given  words,  and  try  out  various  plans  for  connecting 
them.  Something  about  Park  and  Morning.  .  .  .  "The 
park  in  the  morning.  .  .  ."?  No,  we  cannot  make  sense 
that  way.  We  try  again,  bringing  in  Hour  and  We.  "In  an 
hour  we  started  for  the  park  at  early  morning.  .  .  ."? 
No — our  synthesis  is  wrong.  We  have  added  the  word  In. 
We  try  again,  joining  up  Hoiir  and  Morning,  and  this  time — 
perhaps  after  one  other  mistake— we  have  it.  That  Is  to  say, 
we  use  the  trial-and-error  method.  We  adopt  tentatively  one 
mental  pattern  after  another,  until  we  find  one  which  fits. 
Then,  and  then  only,  when  we  have  acquired  insight  into 
the  principle  of  connection,  do  we  succeed. 

(B)  With  Natural  Phenomena. —In  dealing  with  subjects 
of  study  other  than  our  own  thought-made  structures,  we 
are  almost  always  in  this  difficulty.  We  do  not  have  an 
exact  insight  into  laws  of  connection,  and  the  greater  part 
of  the  scientific  work  is  directed  towards  finding  out,  as 
nearly  as  possible,  what  these  laws  are.  We  experiment  with 
our  mental  models,  one  after  another,  until  we  gradually 
attain  to  a  certain  degree  of  insight.  Thus,  when  brought 
into  contact  with  an  interesting  stranger,  we  note  all  his 
peculiarities,  and  then  try  to  put  these  together  in  a  way 
which  will  give  us  insight  into  his  character.  The  optimist 
tend.s  to  .oyntheaise  in  terms  of  prevailing  bias,  and  to  see 
everyone  as  better,  perhaps,  than  he  Is.  The  pessimist  simi- 
larly sees  people   somewhat  worse   than  they   are,   and   In 


AIM  OF  SYNTHESIS 


223 


general,  a  little  consideration  will  assure  us  that,  when  faced 
witl-  a  problem  for  synthesis,  we  combine  the  data  experi- 
mentally, in  terms  of  mental  patterns  which  we  understand 
and  regard  as  helpful. 

There  is,  however,  a  certain  difference  between  thought- 
structures  and  natural  phenomena.    In  dealing  with  thought- 
struc^^ires  we  know  that  there  is  a  key,  and  the  sole  problem 
Is  to  find  it.     In  dealing  with  natural  phenomena,  on  the 
other  hand,  we  assume  that  there  may  be  a  key,  and  a  study 
of  the  history  of  science  will  convince  us  that  we  can,  at  best, 
only  approximate  to  discovering  a  genuine  law  of  connection. 
The  process  of  experimentation  Is  more  prolonged,  and  we 
must  not  expect  it  to  lead  to  a  conclusion  which  will  be  per- 
fectly satisfactory.    We  use  the  best  mental  models  which  we 
know,  and  there  is  no  doubt  that  we  find  these  helpful  In  put- 
ting together  the  data  of  our  various  problems,  but  when  all 
is  said  and  done,  the  mental  model  differs  in  its  structure 
from  the  afitual  phenomena,  and  this  difference  represents  an 
unknown  amount  of  marginal  error.     Thus,  In  dealing  with 
our  fellow-men,  we  can  proceed  on  the  hypothesis  that  they 
are  all  self-centered— egoistic  hedonism  is  the  technical  name 
for  this  model — and  in  general  our  constructions  based  upon 
this  principle  will  be  sufBclently  like  the  structure  of  actual 
motive-complexes  to  "work."     But  a  wide  experience  of  men 
as  well  as  a  less  crude  psychological  theory  will  show  us  that 
the  self-interestPd  man  who  always  acts  upon  calculation  of 
what  will  be  mor*  to  his  advantage  is  a  myth — i.  e.,  a  mental 
fiction,  and  is  noi  found  In  nature.2    Our  models,  then,  are  not 
perfectly  reliable,  and  In  point  of  objectivity  we  can  hardly 
hope  to  realise  the  full  aim  of  synthesis.    We  construct  some- 
thing which  always  differs  from  what  we  wish  to  understand, 
and  our  mental  model  never  quite  fits  Into  the  world  of  actual 
phenomena. 

So  much  for  obJectlvK..  What  are  we  to  say  of  complete- 
ness? The  case  resembles  what  we  discovered  In  dealing  with 
analysis.  Without  Insight  into  the  principle  according  to 
which  the  material  can  be  unified,  we  do  not  really  know 
what  parts  of  the  material  are  relevant  and  what  are  super- 
fluous and  negligible.  In  consequence  of  this  lack  of  insight, 
we  may  unguardedly  omit  something  which  is  vital,  or  add 


«0f.  W.  MacDoagall,  Social  Ptvchotooy,  preface. 


224 


SYNTHESIS 


ItV' 

I 


h 


I  *  ^ 

m 

if 


something  which  is  unnecessary  or  even  misleading.  In  study- 
ing Intelligence,  for  instance,  what  factors  should  he  taken 
into  account  in  our  synthesis,  and  which  elements  should  he 
omitted?  Is  ability  in  mathematical  work,  in  logical  tests, 
and  generally  in  solving  problems,  to  be  estimated  highly, 
while  ability  to  reproduce  strings  of  figures  or  nonsense-sylla- 
bles, and  similar  tests  of  rote  memory,  to  be  estimated  as 
somewhat  of  a  minus  factor,  if  anything?  And  what  are  we 
to  say  of  visual  and  auditory  acuity,  and  in  general  of  good 
powers  of  sense-perception?  Is  their  possession  a  sign  of 
intelligence,  or  not?  Given,  as  data,  answers  to  tests  in  all 
these  fields,  and  the  problem  being  to  synthesise  these  data 
in  such  a  way  as  to  rank  in  order  of  intelligence  the  indi- 
viduals who  have  been  tested,  we  clearly  need  insight  into 
some  principle  which  will  tell  us  which  tests  are  to  be  regarded 
as  important,  and  which  are  to  be  entirely  omitted,  as  of  zero 
or  minus  value  in  estimating  intelligence.  Without  such 
insight,  we  may  blindly  assign  to  sensory  acuity  a  value  equal 
to  that  assigned  to  the  logical  tests,  or  even  assign  a  high 
value  to  the  memory  tests.  In  other  words,  we  may  Include 
in  our  synthesis  elements  which  are  irrelevant  or  even  contra- 
dictory, and  thus  may  seriously  vitiate  our  conclusions.  In 
such  cases  we  can  learn  to  avoid  an  irrationa'  and  external 
completeness,  and  to  approximate  to  a  completeness  which  is 
reasonable,  only  after  much  experimentation  with  mental 
models,  testing  the  tests  themselves,  until  we  find  out  with 
fair  accuracy  which  tests  constitute  genuine  elements,  and 
which  tests  have  a  negligible  value. 

So  also,  on  the  other  hand,  when  evidence  is  scanty,  and  it 
is  necessary  to  add  elements  in  order  to  ronstruct  the  required 
totality,  as  nearly  as  may  be.  Withou'-  insight  into  the  prin- 
ciple in  question,  we  shall  not  know  what  elements  should  be 
added,  and  may  go  seriously  astray.  In  interpreting  the  con- 
duct of  other  persons,  we  have,  as  data  to  be  synthesised,  a 
number  of  observed  actions.  Our  aim  is,  so  to  sum  up  these 
actions  as  to  throw  light  upon  the  whole  system  of  purposes 
and  motives  underlying  a  given  individual's  actions.  Con- 
sider, for  example,  the  character  of  the  emperor  Tiberius.  On 
the  evidence  of  the  bare  actions  recorded  in  history,  we  should 
say,  with  certain  critics,  that  he  was  a  great  administrator 
with  poor  social  qualities,  but  of  a  character  which,  in  the 
main,    was   highly   valuable.     Other   critics,   however,  agree 


METHODS  OF  SCIENTIFIC  SYNTHESIS  225 

with  Tacitus  in  attributing  to  him  a  duplicity  of  purpose 
which  Is  almost  without  parallel  In  the  world's  hlstory.3  His- 
torical reconstruction.  In  general,  lends  itself  to  additions 
here,  and  special  emphases  there,  which  may  or  may  not  be 
justified.  How  far  they  are  scientiflcally  correct,  is  a  matter 
for  careful  weighing  of  the  evidence.  In  cases,  however, 
where  the  evidence  still  remains  indecisive,  suspension  of 
judgment  seems  to  be  the  only  scientific  course. 

In  dealing,  then,  with  natural  phenomena— i.  e.,  with  data 
other  than  mental  models— we  seem  unable  to  attain  to  fiUl 
Insight  Into  a  principle  for  unifying  our  data,  and  thus.  In 
respect  of  both  objectivity  and  completeness,  our  synthesis 
cannot  be  entirely  successful.  There  Is.  however,  no  doubt 
that  we  can  approximate  to  a  synthesis  which  would  be  above 
reproach  by  using  as  mental  models  the  most  approved  pat- 
terns. 

Methods  of  Scientific  Synthesis  (A)  Mathematical.— The 
first  and  most  universal  of  such  patterns  as  are  approved  on 
the  basis  of  experience,  is  the  mathematical  group  of  models. 
Whatever  can  be  counted,  can  be  added  or  syntheslsed,  and  If 
we  can  do  nothing  else,  it  Is  at  least  something  If  we  can 
regard  each  of  our  data  as  approxlmately=l,  2.  3  ...  , 
and  can  thus  proceed  to  add  them,  or  subject  them  to  mathe-' 
matical  manipulation  of  some  more  advanced  kind.  A  stu- 
dent's record  in  college,  for  Instance,  is  expressed  largely  in 
terms  of  this  kind  of  synthesis.  In  a  given  course  there  are 
(Da  number  of  papers.  (2)  a  number  of  recitations,  and  (3) 
a  final  examination,  as  data.  In  most  cases,  the  marking  has 
been  qualitative  rather  than  quantitative.  Recitations,  for 
Instance,  are  good,  poor,  or  fair  average.  Papers  are  A,  B, 
C.  ...  By  assigning  numerical  values  tc  these  data  In 
accordance  with  a  definite  rule,  these  elements  can  be  added, 
weighted,^  and  averaged  in  such  a  way  as  to  satisfy  the' 
demands  of  an  elementary  synthesis.  Such  marking  Is 
admittedly  never  quite  perfect,  but  the  Introduction  of  the 
mathematical  type  of  synthesis  Is  at  least  a  beginning  In  the 
right  direction,  and  Is  far  more  objective  and  complete  than 
a  mere  arbitrary  "general  impression"  would  be.  So  also  In 
the  case  of  the  intelligence  tests  mentioned  above,  and  In  gen- 

sCf.  Furueaux,  edition  of  Tacituti'  Annala.  and  Boliwler,  Tacite 
Lo,^7p^l90.  '"  °*^"'*  ''^  *   "weighted"   average,   see   A.   L.   Jone.. 


yi 


226 


SYNTHESIS 


IV 


£  0  i 


eral,  it  may  be  ntated  that  In  scientific  constructions  we  have 
"science"  in  exact  proper  don  as  our  constructions  foUow 
mathematical  models. 

Such  a  synthesis  in  terms  of  mathematical  models  is  always 
correct  as  far  as  it  goes.  In  most  cases,  however,  it  must  be 
admitted  that  it  goes  only  a  short  way.  It  is  preliminary  to 
a  more  specific  type  of  synthesis.  Its  function  is,  so  to  pre- 
pare the  material,  that  we  can  manipulate  our  data  more 
easily  and  with  a  certain  approximation  towards  insight  into 
the  requisite  principle  of  unification  in  the  specific  case. 
Thus,  in  estimating  the  state  of  prosperity  of  the  country,  if 
the  data — e.  g.,  market  values  of  various  staple  commodities — 
have  already  been  reduced  to  mathematical  form  and  subjected 
to  a  manipulation  which  is  mathematical  and  reduces  them  all 
to  a  common  basis — we  have  alrea4y  advanced  a  long  way 
towards  a  synthesis  which  would  satisfy  economists.  But  in 
order  to  advance  the  whole  way,  we  should  have  to  go  fur- 
ther and  effect  a  synthesis  wh'ch  is  specifically  economical. 
The  mathematician  as  such  cau  handle  data,  but  is  without 
the  specific  insight  into  economical  principles  which  is  requi- 
site for  effecting  a  synthesis  which  shall  fall  within  the  prov- 
ince of  economics.  So  also  in  the  case  of  physics,  or  psy- 
chology, or  sociology.  The  mathematical  synthesis  is  a  nec- 
essary preliminary  to  further  work,  the  final  synthesis  being 
effected  by  a  physicist,  psychologist,  or  sociologist.  In  the 
more  preliminary  stages  of  such  sciences,  the  mathematical 
form  of  synthesis  is  almost  the  only  one  which  is  regarded  as 
legitimate.  But  as  such  sciences  progress  further,  the  merely 
mathematical  synthesis  tends  to  be  regarded  as  a  method 
which  is,  indeed,  universal  and  necessary,  but  is  auxiliary 
and  preliminary  to  the  specific  synthesis  which  it  is  the  aim 
of  the  specific  science  in  question  to  effect. 

(B)  Causal. — A  second  mental  pattern  which,  on  the  basis 
of  experience,  is  thoroughly  approved  for  scientific  purposes, 
is  the  cause-and-effect  model.  Given  as  data, — as  elements  to 
be  synthesised  or  put  together  in  a  way  which  will  make 
sense — events,  processes,  and  generally  data  with  a  temporal 
reference,  it  Is  found  helpful  to  assume,  as  a  mental  pattern 
in  terms  of  which  they  can  be  put  together,  a  rule  according 
to  which  one  event  or  datum  in  time  follows  another.  Mathe- 
matical models  are  employed  as  subsidiary  methods,  in  the 
way  explained  above,  but  in  dealing  with  events,  the  model 


METHODS  OF  SCIENTIFIC  SYNTHESIS         227 

which  exerclaes  a  controlling  influence  is  the  causal.  The 
diagnosis  of  a  case  begins  with  an  exact  analysis  and  tabula- 
tion of  the  data  in  the  form  of  symptoms.  But,  this  analysis 
being  completed,  the  next  step  is  to  put  these  data  together  in 
terms  of  some  mental  model  which  will  throw  light  on  the 
concrete  situation  which  is  the  disease  in  question.  The  sore 
throat,  high  temperature,  etc.,  are  regarded  not  as  mere  units 
which  can  be  added  and  subtracted,  but  as  symptoms— i.  e., 
as  effects  produced  by  some  central  cause,  the  disease  whose 
nature  is  to  be  diagposed.  Certain  phenomena  of  human 
growth  are  explained  as  caused  by  the  direct  activity  of  cer- 
tain glands,  the  rapid  movement  by  which  Dionaea  Muscipula 
secures  its  prey  is  explained  as  caused  by  the  series  of  changes 
Initiated  by  the  lever-like  action  of  the  contact-hairs,  and  in 
general,  the  adoption  of  this  mental  pattern  has  served  to 
unify,  in  a  way  which  makes  sense,  phenomena  the  most 
diverse  in  appearance,  and  data  whose  connection  had  for  cen- 
turies remained  an  unsolved  problem.  The  mathematical  and 
causal  types,  then,  are  among  the  most  universal  and  most 
valuable  of  the  mental  models  by  the  aid  of  which  we  endeavor 
to  make  sense  of  the  world  in  which  we  live. 

Validity  of  These  Methods.— Mental  patterns  for  explaining 
physical  objects  are  seldom  perfectly  adequate  in  point  of 
either  objectivity  or  completeness.  We  have  a  bias  in  the 
direction  of  certain  numbers,  as  when  we  imagine  that  every 
third  wave,  or  every  seventh  or  ninth,  has  the  largest  crest, 
or  when  we  suppose  that  there  are  certain  hidden  rhythms  in 
nature,  which  our  poetic  fancy  can  discover.  So  far  as  causal 
patterns  are  concerned,  there  is  no  human  being  but  frequently 
believes  causation  to  be  at  work  when  there  is,  in  fact,  noth- 
ing but  hallucination.  *  The  belief  in  "ghosts"  as  causal  factors 
in  human  affairs,  in  the  Influence  upon  our  lives  of  "the  stars 
which  shone  at  our  nativity,"  in  our  ability  to  propitiate  the 
forces  of  nature  by  appropriate  ceremonials— all  such  phe- 
nomena indicate  a  hasty  and  improper  use  of  causal  models,s 
and  there  is  no  mental  model  which  is  not  liable  to  such 
unmeaning  or  misleading  usage.  In  themselves,  then,  such 
methods  of  synthesis  are  neither  valid  nor  invalid.  In  respect 
of  validity,  the  sole  question  which  can  be  raised  is,  as  to 
how  we  use  them.     To  this  question,  as  to  the  similar  ques- 


«  Cf.  Herbert  Spencer.  Data  of  Ethics,  chapter  Iv. 


228 


SYNTHESIS 


tion  In  respect  of  analytical  methods,  we  can  give  only  one 
answer.  The  sole  test  of  such  mental  patterns  Is —  Do  they 
"work"?  Do  they  actually  help  us  towards  acquiring  insight 
Into  the  principles  In  accordance  with  which  the  world  in 
which  we  live  seems  to  be  constructed?  Do  they  tend  to 
diminish  the  margin  of  difference  which  separates  the  way 
in  which  we  think  of  things  as  behaving  from  the  way  in 
which  things  are  proved  to  behave,  when  considered  more 
objectively?  Do  they,  that  is,  lead  towards  a  progressive 
insight  into  the  workings  of  nature,  and  thus  help  us  to  under- 
stand and  solve  our  concrete  problems?  If  so,  they  are  so  far 
valid.  If  not,  they  are  worthless,  except  as  sources  of  amuse- 
ment— intellectual  games  which  at  best  do  no  harm,  but  also 
do  not  bring  us  into  touch  with  the  objective  world.* 

Summary. — So  far,  then,  we  have  seen  that  synthesis  is  a 
preliminary  portion  of  scientific  method,  and  that  it  is  of 
universal  application.  Its  aim  is,  so  to  make  use  of  the  bonds 
of  connection  which  hold  data  together,  as  to  put  together  ele- 
ments in  a  way  which  is  both  objective  and  complete.  This 
aim  can  be  fully  realised  when  thought  is  dealing  with  its 
own  constructions,  and  in  such  cases  only.  In  dealing  with 
natural  phenomena,  we  can  only  approximate  to  such  a  syn- 
thesis, by  experimenting  with  mental  models  until  we  find  one 
which  seems  to  apply.  Of  such  models,  the  most  universally 
helpful  are  the  mathematical  and  causal  types.  These  can 
be  regarded  as  valid  so  far  as  they  are  found  to  "work" — i.  e., 
to  help  us  to  escape  from  the  vagaries  of  subjective  imagin- 
ings, and  to  get  into  closer  touch  with  the  objective  world. 
By  such  methods  the  way  is  opened  for  a  synthesis  which 
shall  be  progressively  satisfactory. 

8  The  reference  here  Is  to  the  "dialectical"  method,  bv  which  one 
or  more  persons,  by  consulting  their  own  tuoughts,  would  try  to  snln 
out  of  their  own  heade  a  philosophy  of  nature.  The  method  originated 
with  Plato  (Cf.  the  la.st  half  of  the  Tinweus),  and  Is  well  developed 
In  medlaeviil  science.  Htit  It  Is  not  unknown  In  the  history  of  modern 
thoujrht.  Tlje  iM'st  known  Instances  are  Schclllng's  \a1urphUo»onhU- 
and  certain  of  the  speculations  of  Hegel. 


l!  ^ 

hf 


FOR  FURTHER   READING 
W.  Wundt,  Logik,  (3id  ICdIt.).  Vol.  II,  pp.  8-11. 


EXERCISES 
BXBBCI8BB 


229 


Show  what  part  Is  played  by  synthesis  In  dealing  with  the  follow- 

ng  caaeg:     (1)  m  learning  to  use  the  typewriter.     (2)  If  accidentally 

locked  into  a  room.   In  getting  out.      (3)    In  finding  the  addreas  of 

a  friend  the  other  side  of  town.     (4)   In  estimating  character  in  th« 

2Z  n    "r^'.T":     ^°>   '°  "^'"»  *»"'  ^''^  P'""  '•"•  »  •«'«'»  vegetable 
garden.     (6)  In  keeping  accounts. 


v-V 


iJ^ 


-7 


CHAPTER  XXI 


ANALYSIS  AND  SYNTHESIS 


H'' 


The  Problem. — So  far  we  have  discussed  analysis  and  syn- 
tlie&is  In  separation  from  one  another,  as  though  they  were 
two  sharply  distinct  and  independent  methods,  and  as  though 
each  could  be  applied  by  itself.    In  fact,  they  have  seemed  not 
merely  Independent,  but  even  opposed.     Analysis  means  tak- 
ing apart  by  loosening  a  bond  of  connection.    Synthesis  means 
putting  together  by  introducing  a  bond  of  connection.     And 
yet,  there  have  been  indications  that  perhaps  our  distinction 
was  a  little  sharper  in  theory  than  is  warranted  by  the  actual 
use  of  scientific  method  in  practise.     It  is  doubtful  whether 
any  of  the  instances  we  have  given  can  be  regarded  as  pure 
cases  of  analysis  or  pure  cases  of  synthesis.    For  example.  In 
deciphering  the  message  AAAEB    ....    we  certainly  con- 
atructed  a  complete  cipher  as  part  of  our  process  of  analysis. 
So  also,  in  attempting  to  put  together  the  elements  hour,  for, 
we.  early     ....  we  gave  up  one  attempted  synthesis  after 
another,  on  the  ground  that  they  omitted  certain  of  the  data. 
But   that  certain  of  the   data   were   being  omitted  could   be 
known  only   by   our   analysing   the   totality   which   we   were 
attempting  to  introduce,  and  then  comparing  its  elements  with 
the  given  elements.     That  is  to  say,  so  far  as  our  examples 
go,  they  seem  to  indicate  a  certain  Interconnection  of  analysis 
and  synthesis. 

Again,  if  we  compare  the  procedure,  rather  than  the  exam- 
ples, we  find  that  analysis  and  synthesis  a?ree  in  a  number 
of  essential  points.  Both  proceed  by  the  trial-and-error 
method,  and  by  introducing  mental  models— models  con- 
structed after  a  pattern  which  we  can  understand,  or  take 
to  pieces  and  put  together  again.  That  is  to  say,  the  mental 
models  which  we  use  in  both  cases  as  a  necessary  and  integral 
part  of  the  method  are  themselves  products  of  both  analysis 
and  synthesis— so  that  the  analytical  method  uses  models 
which  are  partly  synthetical,  and  the  synthetical  method  uses 
models  which  are  partly  analytical. 

230 


ANALYSIS  AND  SYNTHESIS 


231 

Finally,  both  methods  have  fundamentally  the  same  aim 
In  order  to  take  apart,  analysis  must  first  discover,  as  nearly 
as  may  be.  what  It  is  which  holds  the  elements  together  In 
order  to  loosen  the  bond  of  connection,  we  must  learn,  If 
possible,  what  that  bond  is.  So  too  with  synthesis.  In  order 
to  put  together,  we  must  haVe  some  unifying  principle,  some 
bond  of  connection,  with  which  to  go  to  work.  Given  ele- 
ments which  are  separate,  they  will  not  fall  together  of  them- 
selves. Some  organising  principle  must  be  introduced,  and  In 
order  to  put  together,  we  must  have  Insight  into  some  such 
principle.  The  primary  aim.  then,  of  both  methods  appears 
to  be  Identical.  Whether  we  wish  to  analyse  or  to  syntheslse 
in  both  cases  tbe  dlBfiOvery  .of  aomcualfylng  principle  con- - 
stltutej  our  primary  aim. 

If  we  now  put  this  evidence  together,  and  realise  that  (1) 
our  examples  seem  to  employ  both  methods.  (2)  the  mental 
models  employed  In  both  procedures  are  both  analytical  and 
synthetical,  and  (3)  the  primary  aim  of  both  methods  is  Iden- 
tical, It  seems  more  than  doubtful  whether  the  previous  sug- 
gestion of  the  Independence  of  the  methods  is  not  to  be  given 
up.  It  looks  as  though  analysis  and  synthesis  are  thoroughly 
Interdependent— as  though  they  should  be  regarded,  not  as 
two  methods,  but  rather  as  two  correlative  aspects  of  a  sin- 
gle method  of  scientific  investigation.  The  problem  of  the 
present  chapter  is  to  examine  more  closely  into  the  relations 
of  analysis  and  synthesis,  in  order  to  discover  whether  there 
are  two  methods,  separate  and  independent,  or  whether  there 
Is  only  a  single  method  with  two  correlative  and  interdepend- 
ent aspects. 

Is  Analysis  Synthetical?  (A)  With  Mind-Made  Entities  — 
Let  us  begin  by  taking  the  analytical  method  and  enquiring 
hew  far  it  essentially  Involves  the  use  of  methods  which  can 
properly  be  called  synthetical.  Suppose  we  find  it  necessary 
to  take  the  lawn-mower  to  pieces.  The  ordinary  procedure  Is 
to  look  it  over,  and  to  examine  it  somewhat  as  follows — 
"These  bolts  are  held  in  place  by  those  nuts.  If  I  loosen  one 
then  this  roller  will  fall  out.  If  I  loosen  both,  then  I  can' 
remove  the  cutting  blade  also.  To  remove  these  revolving 
blades  it  will  be  necessary  also  to  take  off  the  nuts  which 
hold  that  bar  in  place,  etc.,  etc."  That  is  to  say.  in  our  ordi- 
nary and  natural  procedure  with  machinery,  we  certainly  look 
It  over  in  order  to  form  an  idea  a*  to  how  it  is  put  together 


J' 

7 


232 


ANALYSIS  AND  SYNTHESIS 


i! 


:  j; 


In  this  way  we  obtain  an  insight  into  its  structure  which  can 
only  be  called  synthetical.  Even  if  we  fail  to  look  it  over 
as  a  whole,  and  proceed  merely  by  unscrewing  every  nut  and 
screw  In  sight,  and  then  by  pulling  out  every  bolt  until  the 
whole  falls  apart,  we  are  using  an  insight  which  is  synthetical. 
We  act  under  the  impression  that  it  is  screws  and  bolts  which 
are  holding  the  machine  together— i.  e.,  that  it  h<u  been  put 
together  by  these  meaub.  In  dealing  with  machinery,  then, 
with  a  view  to  taking  It  to  pieces,  an  essential  part  of  our 
analytical  method  appears  to  consist  in  considering  how  the 
machine  has  been  put  together— t.  e.,  in  considerations  which 
are  synthetical. 

Let  us  proceed  to  consider  a  second  group  of  entitles  con- 
structed In  accordance  with  a  mental  plan.  We  can  analyse 
a  triangle,  for  instance,  by  taking  it  apart  Into  three  straight 
lines.  Is  there  any  aspect  of  our  method  here  which  should 
be  considered  synthetical?  It  seems  to  resemble  the  machin- 
ery case  just  considered.  We  do  not  know  how  to  go  to  work 
unless  W3  understand  the  principle  which  holds  the  three 
angles  together,  unless,  that  Is,  we  realise  that  three  straight 
lines  must  meet  so  as  to  form  angles  in  such  a  way  that  the 
whole  Is  a  closed  figure.  It  Is  only  when  we  understand  what 
it  is  that  holds  the  triangle  together  that  we  can  take  it  apart 
in  a  way  which  is  both  objective  and  complete. 

If  the  above  cases  may  be  regarded  as  typical,  we  can  state 
that,  in  analysing  structures  put  together  in  accordance  with 
a  plan  devised  by  the  mind  of  man,— i.  e.,  In  cases  where 
thought  is  dealing  with  itself— It  is  necessary  for  us  to  acquire 
Insight  into  the  principle  of  construction  —  a  synthetical 
insight  into  the  way  in  which  such  structures  have  been  put 
together— In  order  to  analyse  in  a  way  which  shall  be  both 
objective  and  complete.  That  is  to  say.  In  such  cases  syn- 
thesis constitutes  an  Integral  portion  of  the  analytical  method. 
(B)  With  Natural  Phenomena.— In  endeavoring  to  analyse 
natural  phenomena,  our  method  Is.  as  we  have  seen,  to  try 
out  one  mental  model  after  another,  with  a  view  to  finding  out 
whether  the  structure  of  such  mental  models  In  any  adequate 
way  corresponds  to  the  structure  of  the  natural  object  which 
we  are  investigating.  That  is  to  say,  we  make  guesses  at  the 
plan  of  structure  of  our  object— we  try  to  think  out  how  It 
might  have  been  put  together,  and  then  see  whether  our  guess 
was  correct,  by  trying  to  take  the  natural  phenomena  apart 


IS  SYNTHESIS  ANALYTICAL? 


233 


in  accordance  with  what  we  auume  to  be  lt«  structural  plan. 
For  example,  in  trying  to  understand  the  atructure  of  tb« 
organ  of  bearing,  the  most  widely  accepted  analysla  it  that 
which  regards  the  basilar  membrane  as  modelled  on  the  struc- 
ture of  the  wires  In  a  grand  piano,  and  in  fact  an  artiflcial 
model  of  Just  such  a  membrane  has  been  made  in  accord- 
ance with  this  prescription.  Other  authorities  try  to  analyse 
it  along  the  lines  of  a  telephone-like  model.i  So  too  in  ana- 
lysing out  the  mechanical  elements  which  enable  a  plant  such 
as  the  bulrush  or  corn  to  withstand  the  pressure  of  the  wind, 
It  la  usual  to  analyse  such  cases  in  terms  of  trusses  and  other 
engineering  models.  That  is  to  say,  in  all  such  cases,  we 
guess  at  the  way  in  which  the  phenomenon  in  question  may 
have  been  put  together,  as  a  necessary  preliminary  to  taking 
It  apart  Our  conclusion,  then,  is,  that  whether  we  are  dealing 
with  the  structures  of  thought  or  with  the  phenomena  of 
nature,  our  analytical  method  contains,  as  an  integral  portion 
of  its  procedure,  the  construction  of  a  model  which  is  taken 
to  represent  the  way  In  which  the  object-to-be-analysed  has 
been  put  together.    Analysis  necessarily  Involves  synthesis. 

Is  Synthesis  Analytical?    (A)  Mind-Made  Entltlea.— Let  us 
now  proceed  to  study  a  little  more  closely  the  method  of  syn- 
thesis.    We  have  before  us  as  data  a  number  of  differently 
shaped  pieces  of  wood,  plus  a  frame— technically  known  as  a 
"form-board."     Our  problem  is,  to  put  these  pieces  of  wood 
together  in  such  a  way  that  they  will  fit  into  the  frame.    We 
look  over  the  pieces  of  wood,  and  then  at  the  place  into  which 
they  are  to  be  fitted.    We  think:— "This  piece  could  go  here, 
these  two  pieces  could  be  Joined  together  so  as  to  go  there,  and 
perhaps  in  this  remaining  space  we  could  put  the  three  or  four 
remaining  pieces."    That  is  to  say,  we  compare  the  space  to 
be  filled  with  the  elements  which  are  to  fill  it.    On  the  one 
hand,  we  see  that  "these  pieces  could  fill  that  space,"  and 
on  the  other,  that  "this  remaining  space  could  be  filled  by 
those   three   remaining   pieces."     In  other   wordb,   when   we 
attend  more  to  the  pieces  and  how  they  might  be  put  together, 
our  procedure  is  more  synthetical.    But  when  we  attend  more 
to  the  space  and  ask  by  what  sort  and  number  of  pieces  it 
could  be  filled,  our  procedure  Is  more  analytical.     We  pro- 
ceed in  this  double  way,  and  there  is  always  some  occasion  for 
comparing  (1)  what  we  want  to  do  and  (2)  the  means  at  our 
disposal.    When  we  make  such  a  comparison,  we  necessarily 
1  Cf.  W.  B.  Plllsbury,  FundammtaU  of  Ptyohology.  pp.  169-170. 


234 


AXALVSIS  AND  SYNTHESIS 


analyi*  wte«t  we  want  to  do,  and  see  how  the  elementa  yielded 
by  thl«  uBiHlyHiH  coiupur*'  with  tht-  mat«Tlal»  which  have  been 
^ul  at  our  iIIbiwswI.  "If  thlB  piece  were  only  a  little  Hhorter. 
it  could  iMi  fitted  In."  That  Ih  to  say.  In  putting  together 
meclwnkal  apparatus,  tmr  aynthetlcal  method  includes  an 
analysiB  of  the  totality  wtilch  we  wish  to  construct. 

htj  too  in  other  caHe.   of  the  same  general  type.     In  solv- 
ing a  problem  i.v   means  of  simultaneous  equations,  we  start 
by  statint;  our  data  in  algebraical  form.    "Let  x=  this,  and 
let   y=  that.     .     .     .      •     But   when   we  come  to  the   work  of 
syn'hesisinK  our  xs  and  ys  so  as  to  represent  in  equational 
form  the  .onditions  which  form  our  data,  there  Is  no  doubt 
thiiL    wf   proceed    in    the   twofold    way   which    we  have  noted 
alMwe      We  keep  one  eye  upon  the  data,  and  the  other  upon 
tlte  eoiuaiional  form  in  which  we  are  trying  to  express  those 
daia.     in  the  whole  procei***  of  trial  and  error   which   culmi- 
n«t*«  m  the  requisite  equations,  we  are  suggesting  one  equa- 
tioaal  <ontent  after  another  and  rejecting  it,  if  its  elements 
differ  irom  the  elements  which  form  our  data,   until   in  the 
end    we   find   one   which  seems  to  satisfy  all   the  conditions. 
That  i.-  to  say,  we  analyse  each  suggested  equational  content 
into  its  elements  in  order  to  compare  them  with  our  data  and 
see  how  far  they  coiuiide.     So  also  if  we  are  called  upon  to 
invent  a  plan  which  will  satisfy  certain  given  conditions,  and 
provide   us   with    a   complete   solution    to   some   examination 
problem  In  ethics  oi    economics.     We  try  one  suggested  plan 
after  another,  analysing  it  in  order  to  discover  whether  the 
conditions  which   it   will    really  satisfy   are  the  same  as  the 
conditions  given  in  the  examination  paper.     In  other  words, 
here  also  our  synthetical  method  Includes  an  analysis  of  the 
totality   which   we  wish   to  construct,  and   if  the.se  instances 
may  be  regarded  as  typical,  we  can  state  that  in  dealing  with 
mind-made  entities  we  always,  as  an  integral  portion  of  our 
synthetical  method,  analyse  the  totality  which  we  are  attempt- 
ing to  construct.     In  such  cases,  then,   synthesis  necessarily 
involves  analysis. 

(B)  With  Natural  f^enomena.— Where  thought  is  not  con- 
fined to  its  own  con-:  uctions,  but  is  attempting  to  get  into 
touch  with  natural  i)rienomena.  what  is  nnr  synthetical  pro- 
cedure? We  try,  as  we  have  already  seen,  to  put  together  our 
data  In  terms  of  some  mental  model,— primarily  of  a  mathe- 
matical or  causal  tyi- — which  is  especially  designed  to  fit  the 


IS  SYNTHF.SIS   ANALYTICAL? 


235 


concrete  situation  ai  nearly  an  possible.  In  order  to  diicover 
whether  It  dois  reaBoutthly  fulfil  the  requlrementi  of  the  •it- 
uatlon,  It  l8,  of  course,  necesHary  to  analyse  the  mental  model, 
and  compare  the  ilements  Into  which  we  dlBsect  It,  with  the 
eleni*>nt8  which  tonstltut*'  our  concrete  data.  For  example, 
given  as  data  the  various  species  of  animals,  and  the  problem 
being  to  put  them  together  In  such  a  way  aa  to  obtain  inaight 
Into  the  principle  of  specification  and  thus  make  sense  of  the 
Infinite  variety  of  nature— how  have  men  proceeded?  The 
older  theory,  (hat  each  speiles  had  been  especially  created, 
resolved  the  whole  question  into  "the  Inscrutable  will  of  the 
Creator, "  and  thus,  In  effect,  gave  up  the  problem.  The  more 
modern  attempts  at  a  solution  In  terms  of  the  evolutlonUt 
hypothesis  very  definitely  consist  In  Introducing  some.mental 
model  of  what  evolution  Is,  and  what  results  It  would  pro- 
duce, if  analysed  «.  ...'fully.  These  results  of  theoretical  anal- 
ysis are  then  carefully  compared  with  the  empirical  facts,  and 
this  Is  the  regular  scientific  method  used  In  dealing  with 
scientific  phenomena.-'  In  other  words.  Ir  dealing  with  either 
mind-made  entitles  or  the  phenomena  studied  In  natural 
science,  our  attempts  at  synthesis  always  contain,  as  an  Inte- 
gral portion  of  their  constructive  nature,  some  degree  of  anal- 
ysis of  the  totalities  which  we  wish  to  construct.  Synthesis 
always  Involves  analysis. 

Summary.— So  far,  our  examination  has  borne  out  the  sug- 
gestions with  which  we  started.  Analysis  Involves  synthesis, 
and  synthesis  Involves  analysis.  There  is  thus  no  sharp  dis- 
tinction to  be  drawn.  There  are  not  two  independent  meth- 
ods, each  of  which  can  be  applied  singly  and  separately.  Anal- 
ysis and  synthesis  are  thoroughly  interdependent,  and  consti- 
tute a  single  method.  There  Is  a  single  analytic-synthetic 
method,  whose  function  Is  to  enable  us  to  obtain  Insight  Into 
the  world  In  which  we  live  by  means  of  taking  apart  and  put- 
ting together  again  phenomena  in  which  we  are  interested.  It 
Is  by  constructing  experimental  models  and  trying  them  out 
in  relation  to  the  actual  phenomena,  that  our  mental  grasp  of 
the  world  grows,  and  It  is  in  this  feature— the  construction  of 
mental  models  for  purposes  of  experimentation— that  we 
should  look  for  th--  ch{«?  characteristic  of  the  method.  For 
this  is  what  both  an  iijsis  and  synthesis  have  In  common.  (1) 
In  respect  of  ultimate  aim— to  understand  the  world  in  which 

'Pti  ,n"t'e/«,lPfture  on  The  Jimionstrathc  Evidence  of  EioluHon 
quoted  in  A.  L.  Jones,  Logic,  pp.  287-300.  aiuiuiwn. 


^ 


m:.m- 


236 


ANALYSIS  AND  SYNTHESIS 


Hi 


we  live, —  (2)  in  respect  of  proximate  aim — to  grasp  the  par- 
ticular principle  of  connection  which  holds  together  a  system 
of  elements  or  concrete  situation  in  which  we  are  interested, 
— and  (3)  in  respect  of  method — the  consiruction  of  mental 
models  which  can  be  taken  apart  and  put  together  again — 
analysis  and  synthesis  are  indistinguishable,  and  are  so  far 
to  be  regarded  as  identical. 

Differences  Between  Analysis  and  Synthesis.— And  yet,  we 
must  be  careful  to  avoid  a  too  hasty  conclusion.    Perhaps  the 
view  which  we  are  taking  may  turn  out  to  be  too  one-sided. 
Analysis   and   synthesis   can   hardly   be   regarded   as   wholly 
identical.    Analysis  has  seemed  more  preliminary,  more  rudi- 
mentary, less  flexible,  less  able  to  take  account  of  rational  con- 
siderations.   It  is  apparently  tied  down  to  the  given  material, 
and  appears  to  be  without  power  of  discrimination,  either  in 
respect  of  omission  of  what  is  Irrelevant,  or  in  the  way  of 
addition  if  some  further  element  is  plainly  demanded  to  com- 
plete a  datum  which  is  fragmentary.    Synthesis,  on  the  other 
hand,  has  seemed  to  be  more  a  completing  of  the  investigatory 
process,  a  summing  up  of  the  results  of  the  Inquiry,  and  a 
final  reconstruction  of  the  principles  which  '  <ive  been  studied. 
It  appears  largely  to  come  after  the  work     .  abstraction  and 
determination,  and  thus  to  be  more  discriminative  than  mere 
analysis.    It  can  apparently  omit  what  is  not  required,  improve 
upon  its  data  in  the  way  of  economy  and  efficiency,  and  even, 
to  a  large  extent,  supplement  its  data  by  completing  curves, 
filling  up  gaps,  extending  applications.     It  seems  of  greater 
efficacy  in  the  positive  or  more  constructive  work  of  organisa- 
tion, and  generally  to  be  a  more  advanced  and  final  repre- 
sentative of  what  we  mean  by  scientific  method. 

Again,  analysis  appears  to  be  easier  than  synthesis.  More 
people  can  take  a  machine  to  pieces  than  can  put  it  together 
again.  Nearly  every  recruit  can  follow  instructions  so  far 
as  taking  his  rifle  apart  is  concerned.  But  when  it  comes 
to  putting  it  together  again,  a  large  percentage  of  the  new 
men  are  driven  to  seek  assistance  from  the  sergeants.  So 
too  any  boy  can  take  a  clock  to  pieces.  But  when  It  comes  to 
putting  It  together  again,  it  has  to  go  back  to  the  clock-maker, 
unless  the  boy  has  a  quite  exceptional  mechanical  ingenuity. 
So  too  many  students  can  follow  a  lecture  in  class  or  read  an 
assignment  at  home,  and  can  take  It  apart  well  enough.  But 
when  It   comes  to   putting  together  again   what  they  thus 


H 
hi 


APPARENT  DIFFERENCES 


237 


studied,  they  frequently  come  upon  unsuspected  difficulties.  It 
looks,  then,  as  though  it  must  be  one  thing  to  take  apart,  and 
another  and  more  difficult  thing  to  put  together. 

(A)  Apparent  Starting-Point. — Let  us  consider,  then,  some- 
what more  closely  the  apparent  differences  between  analysis 
and  synthesis.  In  the  first  place  they  differ  in  respect  of  their 
apparent  starting-point.  The  datum  for  analysis  appears  to 
be  a  complex  totality,  and  the  problem  is,  to  take  this  to 
pieces.    More  exactly,  the  problem  is,  to  find  out  what  are  the 

pieces.     In  the  case  of  the  cipher  AAABH ,  for 

instance,  we  might  suppose  the  elements  ic  question  to  bt  com- 
binations of  A,  combinations  of  B,  or  even  simply  and  ulti- 
mately A  and  B.  But  as  these  suppositions  are  false,  we 
should  in  this  way  be  analysing,  not  the  cipher,  which  is  our 
real  datum,  but  certain  aspects  of  its  mechanism  of  expres- 
sion. In  fact,  the  cipher  is  expressed  in  a  "vay  which  is 
intended  to  conceal  its  real  elements  from  all  but  the  ini- 
tiated. It  is  not  certain  what  t«  the  datum  before  the  analysis 
has  proceeded  some  little  distance.  The  real  datum  is  a  sig- 
nificant message  expressed  in  a  form  intended  to  conceal  its 
real  nature  and  mislead  the  analytical  inyestigator,  and  it  is 
this  datum  which  analysis  has  to  take  apart.  It  is  the  sig- 
nificance which  holds  the  elements  together,  and  it  is  only 
when  our  thought  has  penetrated  some  way  into  this  signifi- 
cance— t.  e.,  only  when  we  have  apprehended  what  the  datum 
is,  that  we  can  avoid  being  misled,  and  can  pick  out  the  gen- 
uine elements.  For  analysis,  then,  the  apparent  datum  is  a 
(rational)  complex,  the  product  of  synthesis. 

For  synthesis,  on  the  other  hand,  the  apparent  starting- 
point  is  a  number  of  disconnected  elements,  which  have  already 
been  analysed  out,  such  as  N,  0,  T,  H,  8,  A,  O,  W,  J,  N,  and 
the  problem  is,  to  put  these  together  in  such  a  way  that  they 
make  sense.  More  exactly,  the  problem  is,  to  reconstruct  the 
original  totality,  to  discover  what  was  the  rational  prmciple 
which  united  into  a  connected  and  meaningful  form,  these 
elements  which  are  apparently  given  as  disconnected.  Here 
again,  however,  there  is  a  difference  between  the  ap*^arent 
and  the  real  datum.  It  is  not  at  first  apparent  what  the 
genuine  datum  is.  It  is  not  Just  a  group  of  letters,  but  it  is 
ten  very  definite  letters  which  are  given  as  elements  which 
together  constitute  a  totality,  i.  e.,  as  elements  which  c&n  be 
rationally  connected  so  as  to  spell  out  a  single  name,  elements 


238 


ANALYSIS  AND  SYNTHESIS 


m. 


which  are  significant,  and  it  is  only  so  far  as  our  thought 
penetrates  into  their  signiflcance — the  meaningful  principle 
which  connects  them  even  in  this  apparently  disconnected 
form — that  we  can  escape  misleading  associations,  and  can 
hope  to  discover  the  totality  in  question.  For  synthesis,  then, 
the  apparent  datum  is  a  (rational)  group  of  elements,  the 
product  of  analysis. 

Thus  we  see,  that  while  both  analysis  and  synthesis  are 
dealing  with  a  datum  which  in  an  ultimate  sense  is  one  and 
the  same — viz.,  a  significant  totality  whose  signiflcance  is  par- 
tially concealed  beneath  its  outward  form — yet  this  ultimate 
datum  is  given  in  two  different-appearing  aspects.  For  anal- 
ysis, the  aspect  which  is  prominent  is  the  totality  or  com- 
plex unity.  For  synthesis,  the  aspect  which  is  prominent  is 
the  scattered,  severed,  plural,  disconnected  form  of  the  data. 
Thus  we  see  that,  while  both  methods  are  ultimately  dealing 
with  one  and  the  same  reality,  the  aspects  of  this  datum 
which  are  most  apparent,  differ  for  analysis  and  synthesis. 

(B)  Apparent  Conclusion. — In  thf  second  place,  the  conclu- 
sion to  which  the  use  of  these  methods  leads,  seems  to  differ 
according  as  we  emphasise  the  analytical  or  the  synthetical 
aspect.  Analysis  starts  with  a  totality  and  concludes  with  a 
disconnected  group  of  elements,  with  elements  whose  plurality 
and  distinct  nature  is  sharply  emphasised.  And  yet,  la  this 
the  whole  conclusion?  It  is  certainly  the  apparent  conclusion, 
but,  if  we  examine  further,  wf  find  that  we  think  of  our  ele- 
ments not  entirely  as  disconnected,  but  partly  also  as  inter- 
connected in  the  totality.  In  analysing  an  argument,  for 
instance,  we  tend  to  group  its  different  steps  as  (1),  (2),  (S), 
....  thus  emphasising,  not  merely  their  distinct  charac- 
ter, but  also  the  fact  that  they  are  each  and  all  steps  in  one 
and  the  same  argument.  That  is  to  say,  the  elements  with 
which  we  conclude  are  not  Just  elements-ln-general,  but  defi- 
nite elements,  elements  of  the  particular  complex  which  fur- 
nished our  starting-point.  The  genuine  conclusion,  then,  is 
not  so  much  a  group  of  elements  as  the  real  nature  of  our 
datum.  Our  conclusion  is  an  analysed  complex — a  totality 
broken  up  into  its  elements  and  held  over  against  those  ele- 
ments by  the  mind,  in  the  general  form  x=^o-f-64-c  .  .  .;. 
In  the  same  way  the  real  conclusion  of  our  analysis  of  the 
bundle  is  not  a  number  of  sticks,  but  the  very  same  sticks 
which  constituted  the  bundle,  plm  the  now  untied  rope  by 


APPARENT  DIFFERENCES 


239 


which  they  had  been  held  together.  There  Is.  then,  a  sharp 
distinction  between  the  genuine  conclusion  and  the  conclusion 
which  is  apparent.  The  apparent  conclusion  of  analysis  is  a 
number  of  disconnected  elements. 

What  is  the  conclusion  of  the  operation  of  synthesis?  We 
start  with  elements  and  we  end — at  least  apparently — with  a 
totality.  At  least  it  is  the  unity,  significance,  and  complex 
individuality  of  our  conclusion  which  are  emphasised.  With  an 
old  pack  of  cards,  if  we  use  a  careful  method  of  inter-weav- 
ing, we  can  create  a  card-house  which  will  not  fall  apart,  and 
which  will  be  the  admiration  of  children.  The  whole  empha- 
sis is  on  the  unity,  strength,  and  consistency  of  the  totality. 
The  whole  emphasis?  Let  us  examine  further.  Is  not  the 
"T.-.nhasIs  always  an  affair  of  contrasts?  Surely  it  is  as  con- 
l.>  ted  with  such  beginnings  that  we  admire  the  conclusion. 
Out  of  such  elements  to  constitute  such  a  totality — that  is 
rather  the  idea  in  our  minds  as  we  contemplate  the  result. 
The  genuine  conclusion,  then,  as  not  the  bare  result,  but 
rather  the  resultant-of-a-method-applied-to-these-deflnite-data. 
Our  conclusion  is  no  mere  x,  but  an  x  which  has  been  con- 
structed out  of  (a+h+c  .  .  .  ;.  Thnt  is  to  say,  while 
superficially  it  might  seem  as  though  tlic  conclusion  of  our 
sjmthetic  process  was  the  bare  totality,  the  genuine  conclusion 
is  the  totality-as-con8truct»>d-out-of-the-data.  Expressed  in  a 
general  formula,  it  is  (a+b+c    ....    )=x. 

Thus  we  see  that  the  genuine  conclusion  at  which  both 
analysis  and  synthesis  arrive  is  the  same.  Both  are  equally 
dealing  with  an  organic  unity,  a  totality  or  individuality  which 
has  two  aspects.  We  can  regard  it  as  a  one-in-many,  as 
a  unity  which  has  also  an  aspect  of  plurality,  as  a  totality 
which  is  composed  of  elements.  Or  on  the  other  hand  we 
can  regard  it  as  a  many-ln-one,  as  a  plurality  which  has  also 
an  aspect  of  unity,  as  elements  which  together  make  up  a 
totality.  We  can  regard  it  either  in  the  form  x=  (a  +  b  +  e 
.  .  .  ),  or  in  the  form  ^o  }-6+r  .  .  .  )=x.  The  reality 
underlying  both  aspects  If  one  and  the  same,  and  it  is  with 
this  reality  that  our  scientific  method  is  trying  to  bring  us 
in  touch.  But  analysis  aims  more  at  expressing  this  reality 
in  the  one  form,  and  synthesis  at  expressing  it  in  the  other. 
So  far  as  we  are  dealing  with  conclusions  which  thus  appear 
different,  we  can  distinguish  analysis  from  synthesis.  But 
80  far  as  these  are  aspects  of  an  underlying  reality  which  la 


^  f 


240 


ANALYSIS  AND  SYNTHESIS 


I    ! 


!1 


one  and  the  same,  analysis  and  synthesis  do  not  difCer  in 
any  fundamental  logical  respect. 

(C)  Apparent  Method.— In  the  second  place,  the  method  we 
use  seems  to  differ  according  as  we  emphasise  its  analytical 
or  its  synthetical  aspect.  So  far  as  we  are  conscious  of  our 
method,  we  believe  that  In  analysis  we  are  taking  to  pieces. 
The  recruit  is  apparently  taking  his  rifle  apart— and  to  a 
mind  which  is  satisfied  with  appearances,  with  aspects  which 
are  prominent,  tl  is  all  that  he  is  doing.  And  yet,  if  we 
look  a  little  furth  ,  it  is  not  dlfBcuIt  to  realise  that  he  is  doing 
more  than  that.  The  whole  point  of  teaching  a  recruit  to  take 
his  rifle  apart  is,  not  merely  that  he  shall  clean  his  weapon, 
but  that  he  shall  acquire  an  insight  into  its  mechanism  which 
he  could  acquire  in  no  other  way.  He  takes  it  apart  in 
order  to  see  how  it  is  put  together,  and  how  it  works.  The 
method  has,  in  fact,  synthetical  as  well  as  analytical  aspects. 
The  true  method  of  analysis,  then,  is  analysis  plus  synthesis, 
usually  in  terms  of  some  mental  model  which  has  both  aspects. 
The  apparent  method,  however,  may  be  regarded  as  merely 
analytical,  merely  taking  tt,  pieces. 

So  too  in  synthesis.  So  far  as  we  are  conscious  of  our 
method,  we  believe  that  in  synthesis  we  are  putting  together 
and  constructing.  The  chief  stress  is  on  the  positive,  build- 
ing-up characteristic  of  the  method.  So  far  as  appearances 
go,  we  are  putting  together  the  pieces  of  wood  so  that  they 
will  fit  into  the  space  in  the  form-board,  and  if  we  are  satis- 
fled  with  the  appearances  which  are  prominent,  this — the 
putting  together — seems  to  be  all.  And  yet,  if  we  look  a 
little  more  closely,  it  is  not  difficult  to  realise  that  at  the 
same  time  as  we  are  putting  together  the  pieces  of  wood,  we 
are  analysing  the  space  which  we  expect  to  fill  with  them. 
The  true  method  is  both  synthetical  and  analytical.  We 
analyse  the  totality  which  we  wish  to  construct,  as  well  as 
synthesising  the  means  at  our  disposal  for  purposes  of  con- 
struction. The  apparent  method,  however,  may  be  treated 
as  merely  synthetical,  merely  putting  together. 

Thus  we  see  that,  so  far  as  the  real  method  is  concern  .  it 
is  the  same,  whether  we  call  it  analytical  or  synthetical.  In 
both  cases  the  method  consists  in  the  analysis  of  a  totality 
into  its  elements  and  the  synthesis  of  elements  into  their 
totality.  The  logical  relation  involves  both  the  relation  of 
parts  to  their  whole,  and  of  a  whole  to  its  parts,  and  this 


IS  SYNTHESIS  MORK  ADVANCED? 


241 


relation  is  fundamentally  the  same  for  both  analysis  and 
synthesis.  The  recruit  who  puts  his  rifle  together  is  at  the 
same  time  learning  to  take  it  apart,  Just  as  in  taking  It 
apart  he  is  at  the  same  time  learning  how  to  put  it  together. 
In  both  cases,  what  he  is  studying  is  the  same— the  relation 
of  the  whole  rifle  to  its  parts,  and  of  the  parts  to  the  whole 
rifle.  He  is  learning  how  the  rifle  works,  and  the  analytical 
and  synthetical  methods  are  two  ways  of  doing  the  same 
thing.  So  far,  then,  they  are  not  to  be  distinguished.  There 
is  only  one  method.  But  It  has  two  aspects,  either  of  which 
can  be  made  prominent.  According  as  the  one  or  the  other 
aspect  is  the  more  prominent,  we  can  distinguish  the  taking- 
apart  aspect  from  the  putting  together  aspect.  In  respect,  then, 
of  the  method  apparently  employed,  we  can  distinguish 
analysis  from  synthesis. 

Is  Synthesis  a  More  Advanced  Method? — In  the  light  of 
these  considerations,  we  should  note  that  it  is  only  when 
speaking  of  the  "apparent"  method8,  that  we  can  regard 
synthesis  as  more  advanced  and  analysis  as  more  preliminary. 
For  example,  analysis  is  not  really  confined  to  Its  data,  but 
in  virtue  of  the  synthesis  Inherent  In  its  method,  can  omit 
or  supplement,  as  far  as  Is  desirable.  Thus,  in  analysing  the 
message  "The  supply  of  game  for  London  is  steadily  going 
up,"  if  we  wish  to  discover  the  elements  which  are  really 
elements  of  the  concealed  message,  nothing  whatever  can  be 
done  with  "supply,"  "of,"  "for,"  "London,"  etc..  These  are 
just  words  added  in  order  to  mislead,  and  form  no  part  of 
the  genuine  message.  It  is  necessary  to  construct  a  mental 
model  for  message-sending  which  shall  emphasise  every  third 
word  only,  filling  up  the  Intervals  with  words  which  seem  to 
make  sense  but  really  conceal  the  meaning  which  is  intended. 
This  mental  model,  which  is  constructed  by  synthesis,  is 
however  the  principle  of  the  cipher,  and  thus  an  analysis 
which  really  analyses  the  cipher — the  genuine  datum — will 
be  an  analysis  which  omits  such  words  as  "supply,"  "of," 
etc.,  and  picks  out  the  first,  fourth,  seventh,  etc.,  words  as 
genuine  elements.  Analysis  Is  thus  not  restricted  to  its 
apparent  datum,  but  can  transcend  this  either  by  way  of 
omission,  or  by  way  of  completion,  if  some  element  is  clearly 
demanded  by  tLj  context  which  our  synthetic  mental  model 
gives  us.  At  the  same  time,  analysis  is  restricted  to  the  true 
datum.    But  then,  the  true  datum  is  the  same  for  synthesis 


242 


ANALYSIS  AND  SYNTHESIS 


I  1- 


also.  Synthesis  transcends  only  the  apparent  datum,  and  is 
rigidly  bound  by  the  true  datum.  Thus,  In  assembling  an 
automobile  from  a  miscellaneous  collection  of  elements,  only 
those  are  selected  which  really  belong  together,  which  can 
be  utilised  in  assembling  a  single  machine.  The  others  are 
rejected,  as  forming  no  part  of  the  true  totality.  In  this 
way,  then,  we  see  that  synthesis  is  not  more  advanced  than 
analysis.  Both  aspects  of  the  analytic-synthetic  method  sUnd 
on  the  same  level. 

Summary.— So  far,  then,  we  realise  that  from  a  standpoint 
which  Is  satisfied  with  appearance,  analysis  and  synthesis  can 
be  sharply  dfstingu'shed  in  respect  of  starting-point,  conclu- 
sion, and  method.  But  If  we  persist  in  looking  beneath  appear- 
ances, we  must  reinforce  our  earlier  conclusions,  and  believe 
that  there  is  only  one  method.  Our  final  conclusion,  then,  is 
that  strictly  speaking  there  is  only  one  fundamental  method 
the  analytic-synthetic  method,  but  that  this  method  has  two 
interdependent  and  correlative  aspects,  of  which  the  one 
consists  in  taking  apart,  and  the  other  In  putting  together, 
and  that  for  practical  purposes  it  may  be  advisable  to  empha- 
sise now  one,  now  the  other,  of  these  aspects.  For  strict 
logical  theory,  however,  it  is  essential  to  realise  that,  whether 
we  wish  to  analyse  or  to  put  together,  we  are  employing  a 
single  fundamental  method,  which  aims  at  understanding  the 
world  In  terms  of  the  part-whole  relation,  the  mental  model 
which  gives  us  the  structure  of  organisation.  Analysis  and 
synthesis  are.  then,  the  two  correlative  aspects  of  a  method 
which  endeavors  to  understand  the  world  in  which  we  live 
as  a  rationally  organised  whole. 


FOR  FURTHER   READINO 

P.  H.  Bradley.  Prlnriplrs  of  LogW.  Bk.  in.  Part  I.  chapter  vi 
H.  Lotte.  Logic,  Bk.  III.     Introduction,  pp.  406-409. 

EXERCISES 

Show  the  Inter-relation  of  analysis  and  synthesis  In  dealing  with 
the  following  cases:  (1)  m  learning  to  sing  or  to  play  on  a  mnsloal 
Instrument.  (2)  In  chooeing  a  new  suit.  (.3)  m  escaping  from  the 
top  floor  of  a  building  In  case  of  Are.  (4)  In  considering  whether 
to  Insure  one's  life  or  not.  (H)  In  translating  from  a  foreign  lan- 
suage.  6)  In  estimating  one's  pa-obable  expenditure  for  the  next 
month  or  year. 


CHAPTER  XXII 


ABSTRACTION 

"One  thing  at  a  time"  is  the  motto  of  abstraction      By  its 
aid  we  can  consider  an  acquaintance  from  the  sole  standpoint 
of  personal  appearance,  or  commercial  standing,  or  political 
leanings,  or  church  membership.     We  can  select  friends  on 
the  basis  of  golf-playlng.  to  the  total  neglect  of  other  charac- 
teristics, or  of  interest  in  music,  art,  public  service,  or  what 
not.     In  every  day  life,  it3  use  is  sometimes  helpful,  some- 
times harmful.     But   for  purposes  of  scientific   Investigation 
Its  importance  is  vital.    Unless  we  could  deal  with  one  aspect 
at  one  time,  any  subject  at  all  complex  would  be  hopelessly 
beyond  our  understanding.     But  when  we  divide  It  up    and 
consider  a  single  aspect  at  a  time,  something  can  be  done     It 
is  by  the  aid  of  abstraction  that  the  division  of  labor  is  pos- 
sible, one  worker  tackling  one  part  of  a  task,  and  another 
concen  ratmg  his  energies   upon  another  part,  and  it  is  by 
this   division    of   labor    that    complex   and    highly   developed 
results  are  possible,  in  commercial  life  or  in  science.    Abstrac- 
ion  is  thus  one  of  the  watchwords  of  scientific  management 
It  is  one  of  the  chief  elements  in  organ. sation 
n,.1!;«r  T.**'    ^''•*'^"=*">"-Abstraction    is    no    preliminary 
method.    It  presupposes  both  analysis  and  synthesis,  and  may 
be  regarded  as  a  further  development  of  the  analytic-synthetic 
method.     Its  starting-point  is  no  concrete  situation  given  In 
nature,  but  a  situation  which  has  already  been  analysed  out 
into  a  number  of  different  factors.     Let  the  starting-point  be 
symbolised  by  x  =  (a+b  +  c).    Abstraction  proceeds  by  tak- 
ing out  of  Its  context  any  one  of  these  elements,  a  or  6  or  c 
and   deliberately   neglecting   the   others.     Abstraction   means' 
taktng  out  of  its  context.    It  is  thus  a  highly  artificial  process 
and  leads  to  a  highly  artificial  result.     When  we  say  that  a 
statement  is  "abstract,"  we  usually  mean  that  It  is  artificial 
and  cut  off  from  the  actual  flow  of  experience  as  experience 
IS  given  to  ug. 

Abstraction,  then,  is  the  exclusive  concentration  of  atten- 

243 


-v'-. 


•>■-  1 


X 


AK-Ty 


rfi- 


/ 


M4 


ABSTRACTION 


tlon  upon  some  one  element  of  a  complex  whole.    Ita  nature 
is  thus  negative  as  well  as  positive.    Negatively  regarded,  It 
excludes  rigidly  every  suggestion  of  natural  context.     The 
statistician  considers  people  merely  as  so  many  numbers  in 
the  "population."     The  politician  considers  them  merely  as 
BO  many  potential  votes  for  or  against  himself  or  his  party. 
Both  exclude   from   consideration   the   rich  professional  and 
domestic  Interests  and  activities  of  the  individuals  in  question. 
So   too  a  salesman's  chief  business   is  to  "get  orders,"  an 
artist's  chief  business  is  to  paint  pictures,  etc.    Abstraction 
thus  excludes  breadth  of  vision  and  confines  itself  to  a  rigidly 
narrow  outlook.     On  the  other  hand,  however,  this  narrow- 
ness has  certain  positive  merits.    The  outlook  of  abstraction 
is   intensive,   and   makes   for  efficiency.     It  not  only   takes 
away,  but  It  gives  something  new.    When  we  abstract,  we  do 
not   merely   cut  off  an  element   from   its  context.     It  i*.  of 
course,  cut  off,  but  the  mind  proceeds  to  fix  it,  to  give  it  a 
certain  self-subsistence,  to  give  it  an  independent  nature  and 
unity  of  its  own— which,  amongst  other  things,  can  be  named. 
"Whiteness,"   "softness,"   "depth,"   ticklishness,"    "individual- 
Ity,"  etc.,  are  abstract  qualities,  qualities  taken  out  of  their 
original  contexts  and  endowed  with  a  certain  kind  of  being 
peculiar  to  themselves.     The  entities  to  which  our  scientific 
concepts  and  laws  In  the  first  Instance  apply,  are  one  and  all 
of  this  abstract  and  artificial,  half  mind-made  kind.     They 
are  taken  out  of  their  natural  contexts  In  experience  and  are 
endowed  with  a  new  nature  and  unity.    The  nature  of  abstrac- 
tion, then,  is  to  take  out  of  its  context  a  single  element,  or 
group  of  elements,  and  to  endow  this  entity  with  an  artificial 
kind  of  self-subsistent  being. 

Aim  of  Abstravtion:  (A)  Objectivity.— What  precisely  Is 
our  aim  oi  intention  in  abstracting  aspects  or  elements  from 
their  contexts?  In  the  first  pk:e,  we  aim  at  objectivity.  The 
whole  point  of  abstracting  is  to  bring  ourselves  into  still 
closer  contact  with  objective  reality  than  is  possible  by  the 
use  of  analysis  and  synthesis  alone.  It  is  because  we  are 
helpless  In  the  face  of  nature  taken  as  a  whole,  that  we 
endeavor  to  proceed  piecemeal,  taking  one  small  problem  at  a 
time  and  breaking  up  our  analysed  totality  into  elements 
which  we  can  examine  separately,  and  thus  proceed  gradually 
to  understand  the  whole.    If  we  wish,  for  Instance,  to  study 


AIM  OF  ABSTRACTION 


245 


memory,  we  immediately  discover  that  the  subject  Is  far  too 
wide  to  be  grasped  all  at  once.    Accordingly,  we  narrow  It 
down,  first  to  mechanical  or  rote  memory,  then  still  further, 
until   finally  we  begin  to  direct  our  experimental  attention 
upon  some  such  problem  as  "How  many  repetitions  does  It 
take  to  learn  a  series  of  twelve  nonsense-syllables"?  or  "What 
part  does  such  and  such  a  rhythm  play  in  helping  us  to  learn 
such  a  series"?  or  "Does  learning  a  series  in  the  forward 
direction  help  or  hinder  learning  it  in  the  reverse  direction"? 
It  is  only  after  solving  an  enormous  number  of  such  narrow 
and  special  problems  that  we  can  begin  to  approach  the  more 
general  questions  connected  with  remembering.     That  is  to 
say,  abstraction  brings  us  into  closer  and  more  intimate  con- 
tact with  the  subject  which  we  wish  to  study.    So  too  if  we 
wish  to  acquire  mastery  over  some  musical  instrument,  we 
can,  It  is  true,  attain  to  a  certain  level  of  general  accomplish- 
ment by  Just  playing  anything  and  everything  in  which  we 
are  interested.     But  there  comes  a  time  when  we  have  to 
choose  between  remaining  at  this  low  level,  and  giving  up 
our  interesting  flhow-pleces  in  favor  of  technical  studies,  each 
of  which  is  designed  to  assist  us  in  acquiring  some  small 
and   special   point   of   execution.     We   practise   a   school   of 
velocity,  an  art  of  finger-dexterity,  a  volume  of  octave-atudiea, 
etc.,  and  this  concentration  of  attention  upon  one  point  at  a 
time  helps  us  to  work  our  way  into  the  subject  itself,  to  become 
acquainted  with  its  difficulties  and  its  peculiarities.     But  for 
the  fact  that  our  scientific  insight  and  artistic  execution  sens- 
ibly improve  by   the   use  of  this  method,  we  should  never 
abstract  and  substitute  a  study  which  is  dull  and  dry  for 
the  living  reality.     If  it  were  not  that  we  actually  feel  our 
way  better  and  more  surely  into  the  subject  studied  by  this 
method,   we   should   never  apply   ourselves   to   mathematics, 
grammar,  or  logic,  but  should  be  like  the  young  Deities  of 
romance,   knowing   all    things    by    the    sheer   might   of   our 
minds.    Our  primary  aim,  then,  in  abstracting,  is  objectivity. 
(B)    Completeness. — A    secondary    aim,    which   is    always 
before  us  when  we  abstract,  is  a  certain  kind  of  complete- 
ness.    At  first  sight   it   might   seem   as   though  abstraction 
explicitly  avoided  completeness,  because  it  aims  at  fragmen- 
tarlness,  at  producing  incompleteness,  at  Isolating  some  ele- 
ment and  separating  it  from  the  context  which  completes  it. 
This  is,  indeed,  true,  but  is  not  quite  what  is  meant.     It  is 


l1  1 


w 


hi 


M6 


ARSTRACTrO.V 


«t   the   complete   Igolatlon   of   thJH   nleinent   that   abstuutlon 
alms.     Negatively,  the  context  or  tontexts  in  which  such  an 
element  is  found  must  be  Htrippe.t  off  and  ex.luded  trom  con- 
•  deration,  and  this  is  to  be  ,  an  led  Ihrou^h  .(..npletely.     Posi- 
tively   the  element  which  Is  thus  i.solate.l  Ih  to  be  fully  repre- 
•ented  In   its  ow     nature.   In  complete  Independence  of  Its 
original   context   or   contexts.     The   element   thus   abstracted 
Is  to  be  understood  and  studied  in  its  .on.plete  nature,  so  far 
as  this  Is  possible.    This  means  In  practise,  that  the  element 
n  question  must  be  abstracted  from  a  variety  of  different  con- 
texts.  In  order  that  we  may  escape  from  one-sidedneH.^    ,nd  may 
take  a  complete  view  of  the  element  which  we  are  ab.Macting 
Thus     n  studying  the  question  as  to  whether  Yellow  Is  "slm^ 
pie     like  red.  green,  and  blue,  or     composite"  like  purple    it 
IB   usual    to  experiment    with   sunlight,    w'-h   gaslight     with 
electric  light,  vtc.-i.  ,-.,  with  a  Yellow  drawn  from  as  great 
a  variety  of  sources  as  possible.     So  too  in  siudylng  in  what 
sense    an    author    uses    a    particular    expresslon-c.    „      whu 
Aristotle    understands    by    -nature.  •   or   Kant   bv    ••conscious- 
nes8-ln-generar-lt  is  usual  to  put  togcher  all  ."he  instances 
taken  from  a  wide  range  of  contexts,  in  order  to  avoid  one- 
sided  errors  and  to  attain  to  a  complete  view 

How  Far  Realisable?    (A)     With  Mind-Made  Entitiea.-How 
far  can  this  aim  be  realised?     That  is  to  say.  how  far  can 
we   while  completely  singling  out  and  separating  from  its  eon- 
text  some  aspect  of  a  larger  whole,  attain  to  objectivity'    Let 
us   see.      In   dealing   with    a    complicated   electrical    machine 
which  refuses  to  work,  we  try  to  discover  what  is  wrong  by 
he  method  of  abstraction.     We  single  out   for  special   test- 
ng  one  contact  after  another,  until  we  find  where  it  Is  that 
the  current  Is  broken.     Each  case  of  singling  out  Is  here  a 
single  abstraction,  and  our  method  is  certainlv  objective   For 
t   dea  s   with   special   elements   which   analysis  discovers   in 
the  object  Itself.     The  contacts  are  parts  of  the  machine,  and 
they    are    the    parts    which    It    is    Important  to  investigate 
Whether  our   abstraction   is  complete  or   not.   depends   upon 
the  way  in  which  we  deal  with  each  individual  contact      It 
18  certainly  possible  to  Isolate  It  from  the  rest  of  the  machine 
and  to  test  It  completely  with  full  reference  to  Its  objective 
nature.     If  this  case  may  be  regarded  as  tvpl^.^l,  th^n    we 
can  state  that  in  dealing  with  machines  our  abstraction' can 
be  both  objective  and  complete. 


AIM  OF  ABSTRACTION 


247 


Let  U8  consider  another  example.  In  looking  over  a  system 
of  shorthand,  or  in  estimating  the  claims  of  some  new  arti- 
ficial language,  it  is  possible  to  concentrate  attention  exclu- 
sively upon  some  particular  feature — e.  g.,  with  a  view  to 
improving  and  simplifying  it.  In  all  such  cases,  i.  e.,  where 
thought  is  dealing  with  Its  own  constructions,  our  abstraction 
can  be  objective — for  it  is  directed  upon  some  particular  sign 
in  shorthand,  or  upon  some  particular  rule  in  the  artificial 
language,  etc.  Whether  it  Is  complete  or  not,  appears  also 
to  be  in  our  power,  it  is  merely  a  question  of  studying  our 
subject  carefully,  avoiding  misleading  associations  and  con- 
centrating our  attention  upon  what  is  before  us.  If  these 
instances  are  typical,  we  can  say  that,  in  dealing  with  mind- 
made  entities,  our  abstraction  can  realise  Us  aim  in  point 
of  objectivity  and  completeness. 

(B)  With  Natural  Phenomena.— As  has  been  already  stated, 
abstraction  is  no  preliminary  method,  but  starts  with  a  datum 
which  has  already  been  analysed,  and  proceeds  to  concentrate 
attention  upon  some  one  of  the  elements  revealed  by  analysis. 
It  is  therefore  with  a  mental  model,  rather  than  with  the 
natural  phenomenon  itself,  that  we  are  more  immediately 
concerned  in  abstraction.  But  even  here,  the  chief  value  of 
the  method  Is  that  it  brings  us  into  closer  connection  with 
the  objec  ive  facts  than  would  be  possible  without  its  aid. 
Let  us  consider  an  example.  J.  Chr.  Wolff's  Paychologia 
Empirica  is  a  product  of  analysis  and  synthesis.  If,  however, 
we  »  sh  to  test  its  objective  significance,  we  concentrate 
attention  upon  some  special  "proposition"  or  group  of  "propo- 
sitions." Let  us  take  one.  Wolff  asserts  that  the  laws  of 
waking  life  are  diametrically  opposed  to  the  laws  of  dream- 
life,  so  that,  whereas  waking  life  is  rational,  deliberate,  etc., 
the  dream-life  is  irrational,  and  does  not  admit  of  delibera- 
tion, choice,  etc.  We  test  this  case  by  bringing  special  experi- 
ments to  bear.  We  test  the  laws  of  association— they  seem 
to  be  fundamentally  the  same  in  both  cases.  We  make  exper- 
iments upon  reasoning.  These  also  give  similar  results,  for 
many  dreamers  solve  mathematical  problems.  We  test  delib- 
eration and  choice.  Many  dreamers  deliberate,  and  many 
dreamers  exercise  choice  and  volition.  After  making  a  large 
number  of  experiments  of  this  general  type,  we  find  ourselves 
much  closer  to  the  objective  facts  than  we  were  by  rea(fing 
and  accepting  the  system  of  Wolff.     In  dealing  with  natural 


248 


A  FiSTR  ACTION 


ph^omena.  it  la  precisely  by  such  Bpedallsed  observation,  and 

the  object  ve  facts.    That  we  can  attain  to  complete  objectiv- 
ity in  dealing  with  such  facts.  Is  not  claimed.     But  that  we 

aid  iTnT'"  ""^  °'-"'"''  *••"""  "P°°  '^^  ^'<"-'''°«»  0'  nature, 
o^t  Z,  TTh   'h  '"^««"'^^">'-*-  --  progressively  and  with- 
out lln,  t-l,y  the  help  of  abstraction,  there  can  be  no  doubt 
Completeness  in  any  final  sense,  when  we  are  dealing  with 
natural  ,»henomena.  is  perhaps  out  of  the  question.     We  col- 
lect  as  great  a  variety  of  instances  of  the  aspect  of  our  phe- 
■omenon  under  study,  as  is  possible  for  us,  and  endeavoi    by 
comparing   these  with  one  another,  to  escape   the  dange^  of 
one-8tded*^s   and    to    make   our   abstraction   complete      But 
hat  w.   can  do  more  than  approximate  to  this  aim.  appears 
inu>robable.     For   example,   in   psychology,   we  Us    to  experl- 
men    upon  attention,  or  memory  or  reasoning,  and  upon  some 
special  point  In  one  of  these  fields,  to  the  complete.  Lcluslon 
of  ev-ery  point  other  than  the  one  we  wish   to  study      This 
complete    exclusion    cannot    however,    as    a    rule    be    accom- 
pllBhed.  and  thus  we  have  to  content  ourselves  with  taklnir  a 
number  of  instances  of  our  phenomenon  from  different  angles 
of  approach,  and.  by  putting  these  together,  to  eliminate  the 
elements   peculiar   to   each   case   and   thus  obtain   something 
like  a  concentrated.  Intensive  view  of  the  common  elements 
present  in  each  case-elements  which  are  more  directly  con- 
nected with  the  problem  under  study.     By  studying  the  phe- 
nomenon now  in  this  context,  now  in  that,  we  are  enabled  to 
loo8«n  somewhat  its  connections  with  any  particular  context 

T^IT     I '"  "■"'""  '°  *''"  ''  ''  «P«'-^  ^'•«'"  the  contexts 
in  which  we  have  experienced  it.    This  Is  an  indirect  method 
of  abstraction    and   is  found   helpful   in  direct   proportion  to 
the    variety    of    the    instances    compared.      But    a    complete 
abstraction  i.  hardly  attainable  by  such  means.     However    by 
concentrating  our  attention,  as  far  as  possible,  upon  a  single 
aspect  at  a  time-as  in  some  of  our  more  specialised  Intelll- 
genre  tests-it  is  possible  to  Improve  our  methods  of  experi- 
mentation,   and    gradually    to    revise    the    generally    adopted 
mental  models  with  which  work  is  done  in  such  fields.  Abstrac 
.on.  then,  though  not  perfectly  complete,  is  a  method  which 
leads   to    progressive    improvement    In    .lealine   «.»),    53f„ra' 
phenomena.  In  respect  of  objectivity.  '^ 

Type,  of  Abttraction  (A)   Iwlation.-So  far  we  have  smq 


TYPES  OF  ABSTRACTION  $9 

that  abstraction  iis  a  method  of  separating  from  its  context 
some  aspect  of  a  phenomenon  In  which  we  are  Interested,  and 
It  might  seem   as   though   abstraction,  as  such,  mutt  be  a 
method  of  isolation,     it  is  usual,  however,  to  distinguish  two 
main   types,   (i)   iHolatlon,  and   (2)   generalisation.     When  a 
machine  such  as  a  telephone  refuHes  to  work,  the  repairer 
takes  one  fuse  at  a  timt',  and  proceeds  from  one  contact  to 
the  next,  testing  eaeh  one  until  he  discovers  the  cause  of  the 
difficulty  in  question.     That  is  to  say.  he  proceeds  very  def- 
initely by  a  method  of  isolation.     He  takes  each  contact  by 
itself,  and   tests  it   to  see  whether  it   is  In   working  order, 
without  any  reference  to  the  rest  of  the  mechanism.     That 
is  an  Hxamplo  of  the  method  of  isolating  abstraction.    So  too,  If 
In  trying  to  play  a  difflcult  study  a  music  student  finds  ther« 
is  some  point  of  technique  which   is  beyond  his  immediaw 
powers,  he  practises  that  particular  point  of  technique— f.  g., 
the  trill  or  mordent— by  means  of  specialised  studies  until  he 
huH  mastered    it.      It    is    by    gpeclalisatlon.    or    by    isolating 
abstraction,  that  he  overcomes  his  difficulties.     This  Instance 
differs  slightly  from   the  telephone    case.      In    i^eallng    with 
machinery,   we   Isolate   a   single   Instance,  and   are   satisfied 
with  that.     In  practising  so  as  to  learn  to  execute  the  trill, 
we  spedalise  on  that  general  kind  of  finger-movement,  and 
practise  as  great  a  variety  of  trill-studies  as  possible,  so  as 
to  be  able  to  play  the  trill  in  whatever  kind  of  context  we 
may  happen  to  meet  it.     That  is  to  say.  in  this  type  of  case 
we  Isolate  by  taking  as  many  varieties  of  the  phenomenon 
under  study  as  possible.     Theie  is,  however,  no  difference  in 
principle   between   the  two  types  of  Instance.     All   isolation 
Is  with  a  view   to  specialised   study,  and  both   varieties  of 
isolation  illustrate  the  principle  of  abstraction. 

(B)  Generalisation.— (leneralisatlon  is  not.  in  principle, 
different  from  Isolating  abstraction.  But  from  a  superflclal 
standpoint  It  certainly  appears  different  For  instance.  It 
seems  to  lead  to  a  different  kind  of  result.  Most  empirical 
laws,  e.  g.,  are  generalisations  from  a  number  of  experiences. 
We  find  that  graduate  students  in  psychology  can,  as  a  gen- 
eral rule,  learn  a  series  of  twelve  nonsense-syllables  in  from 
seven  to  nine  repetitions.  We  put  together  the  results  of 
several  distinct  observations  based  upon  certain  further 
experiments  of  this  general  type,  and  gradually  construct  a 
memory  curve,  a  learning  curve,  a  practise  curve,  etc.    Bach 


w 


r. 


-^■^'. 


2S0 


ABSTRACTION 


of  these  is  a  generalisation  on  the  basis  of  repeated  experi- 
ence. Thus  we  see  that  not  only  the  pre  Ucal  wisdom  which 
accumulated  experience  of  men  and  .^s  brings  with  It. 
but  also  most  of  the  concepts  and  l&v,  empirical  science, 
are  products  of  generalising  abstraction  vV'e  arrive  at  such 
generalisations  by  Isolating,  so  far  as  w.  can.  instances  of 
tftj  special  phenomenon  under  study,  in  order  to  eliminate 
what  is  Irrelevant  to  our  purposes,  and  thus  from  a  variety  of 
instances  extract  the  composite  result  which  we  call  a  gen- 
era Isation.  Like  the  more  complex  cases  of  isolation,  gen- 
eralisations are  thus  products  of  an  abstraction  which  works 
by  isolating  special  aspects  of  phenomena  in  which  we  are 
Interested. 

Validity  of  These  Methods.-There  is  nothing  sacrosanct 
about  abstraction  in  any  of  its  forms.     Isolation  always  has 
Its  dangers.     In  separating  some  particular  aspect  from  its 
context,  it  is  peculiarly  easy  to  omit  something  vital  or  to 
ado  something  which  is  Irrelevant.     Too  much  attention  to 
detail,    e.    g.,    in    literature,    prevents    our    appreciating   the 
whole,  and  it  is  often  that  we  fall  to  see  the  wood  because 
we  direct  our  attention  too  exclusively  upon  particular  trees 
So  too  generalisations  are  often  hasty  and  erroneous,  the  pro- 
ducts, as  we  say.  of  a  "vicious"  abstraction.     Thus    in  what 
,  is  known  as  "Faculty  psychology-which  represents  a  gen- 
eral tendency,  rather  than  any  definite  school-we  regard  our 
minds  as  consisting  somehow  of  a  number  of  distinct  "facul- 
ties." such  as  Memory.  Reasoning.  Will,  Emotion.  Sensation 
etc.i     That  is  to  say.  we  come  to  regard  what  wc  have  taken 
apart  into  elements  is  though  in  itself  it  consisted  of  a  num- 
her   of  distinct    elements.      Such    "hypostatisation."   as    it    is 
called,   is  the  peculiar  danger  of  abstraction,  and  is  a  com- 
mon source  of  error  in  all  the  mental  sciences. 

Abstraction,  then,  is  sometimes  invalid.  On  what  does  its 
validity,  when  it  is  valid,  depend?  It  is  valid  only  so  far  as 
It  leads  to  progress  in  obtaining  insight  into  the  workings 
.  of  the  phenomena  in  which  we  are  interested.  So  far  as  it 
leads  to  a  definite  advance  in  fientiflc  knowledge.  It  is  valid 
But  it  must  always  be  remembered  that  what  we  separate 
for   purposes   of    special    experimentation,    is   given   together 

^t^\7'%Kl^n"^^   b".  "»"""*  Vndrr»tandino.   Itk    II    rhaoter  ixl 


EXERCISES 


251 


with  various  other  elements,  and  that  It  may  be  fatal  to 
regard  as  separate  in  itself  what  we  have  found  useful  for  our 
special  purposes  to  regard  as  so  far  separate  and  distinct. 
In  dealing  with  natural  phenomena  especially,  abstraction 
Is  very  seldom  fully  valid,  but  may  be  regarded  as  Justlflable 
so  far  as  it  leads  to  greater  knowledge  of  the  objective  facts 
studied. 

Summary.— In  all  its  typical  forms,  abstraction  is  a  method 
of  taking,  from  the  context  in  which  it  is  embedded,  some 
aspect  of  a  phenomenon  In  which  we  are  Interested.  Nega- 
tively, the  context  is  eliminated  and  stripped  off,  so  far  as 
this  is  possible.  Positively,  the  special  aspect  studied  Is  given 
a  certain  unity  and  self-subsistency  by  the  mind,  which  not 
only  cuts  it  off  from  its  context,  but  fixes  and  names  it.a 
Although  the  action  of  our  mind  in  to  some  extent  arbitrary— 
for  we  select  for  study  any  aspect  whatever  In  which  we 
happen  to  feel  Interested— we  yet  aim  at  objectivity,  and 
endeavor  ♦<>  make  our  abstraction  c«.  mplete.  In  dealing  with 
mind-maa.  entities,  this  aim  can  be  realised.  In  dealing 
with  natural  phenomena,  it  can  be  realised  only  approxi- 
mately. In  all  cases,  however,  the  method  of  taking  one 
thing  at  a  time  leads,  or  tends  to  lead,  towards  attaining  to 
greater  insight  into  the  workings  of  the  phenomenon  under 
study,  and  abstraction  is  thus,  as  a  scientific  method,  progres- 
sive and  fruitful  In  results. 


2  Hence  the  dantrer  of  hypoHtatisatlnn. 


FOU  FtriTIIER   HEADING 

B.  Hosanquwt.  Los/ir.  Vol.  11.  pp.  2l-L'4.  U.  Krdmann.  lAtf/ik.  (2nd 
Kdlr.t.  pp.  0.-I-7H.  88-!>l'.  Chr.  Sluwait.  Louie.  Vol.  I.  pp.  'J-IS-L-.-iO : 
Vol.   11.  pp.  C«MI!».     \V.  WuiKlt.  Lofiik.  (.-{ril  Edit.l.  pp.  11-17. 


KXEUCISES 

Show  what  part  Is  played  by  abdtracflon  In  denllnjt  with  the 
following  caMes:  d)  m  flndlng  out  what  has  caused  a  headai-he. 
Cit  In  leainlnB  a  new  dan<e.  CO  In  translailnu  from  a  foreign 
langHage.  (4»  In  correctlnjt  papera  In  a  high  mhixil  HUbJeit.  (5) 
In  selettlnK  a  dinner  from  a  menu.ard.      (fl)   In  chotmlnjc  a  career. 


CHAPTER  XXIII 


f 


DETERMINATION 

Nature  of  Determination.— Determination  is  the  reverse  of 
abstraction.    Abstraction  takes  a  single  element  out  of  its  con- 
text and  isolates  it  as  strictly  as  may  be,  treating  it  by  Itseif. 
Determination  takes  an  isolated  element  out  of  its  isolation 
an*!  places  It,  as  far  as  pcasible,  in  a  context  to  which  It  is 
adapted.      In    rare   cases    determination    exactly    reverses    an 
abstraction,  and  replaces  an  element  In  the  precise  context 
from  which  abstraction  had  taken  it.    But  as  a  general  rule, 
starting  with  an  element  which  has  been  thoroughly  loosed 
from  its  original  context,  we  proceed  to  determine  it  by  plac 
ing  it  in  a  variety  of  contexts  which  happen  to  suit  our  pur- 
poses, whether  the  element  in  question  has  previously  formed 
part  of  such  contexts  or  not.     For  Instance,  starting  with  a 
single  muscle,  which  abstraction  has  Isolated  from  its  place 
in  e.  {jr.,  the  frog,  we  proceed  to  determine  the  nature  of  mus- 
cular action  by  placing  it   upon   an  electrical   machine  and 
galvanising  It  into  activity   until   It  is  thoroughly  fatigued. 
In  this  case  we  place  It  In  a  context  in  which  it  has  never 
formed  a  part,  but  which  throws  considerable  light  upon  its 
workings.    So  too  In  studying  memory.  We  start  with  abstract 
entities  such  as  nonsense  syllables,  and  by  learning  these  In 
various  types  of  context  of  which  it  is  safe  to  say  they  never 
naturally  formed  part,  we  proceed  to  determine  our  memory 
of  them  in  a  way  which  has  led  to  a  number  of  remarkable 
discoveries  as  to  the  workings  of  memory. 

Results  of  this  type  are,  however,  in  themselves  still  stmie- 
what  abstract;  and  determination  proceeds  to  make  their 
more  concrete  by  placing  them  In  contexts  which  more  nearly 
approach  the  conditions  of  actual  life.  Thus,  we  consider 
how  muscular  action  becomes  modihed  whi.h  we  have,  not 
an  isolated  muscle  functioning  by  Itself,  but  when  we  have 
several  muscles  working  together  in  the  organism  in  a  whole. 
Our  earlier  results  with  the  electrical  machine  become  con 
siderably  modified.    We  learn,  for  instance,  that  in  the  11-., ag 

252 


AwjiJfr 


^H-' 


\^^1 


NATURE  OF  DETERMINATION 


2S3 


organism  no  muscle  ever  becomes  completely  fatigued,  and 
that  fatigue  seems  to  be  a  matter  of  attention  rather  than  of 
the  muscles  as  such.  So  too  the  nonsense-syllable  results  are 
not,  as  such,  immediately  applicable  to  material  which  has 
meaning  for  us,  and  become  determined  in  a  variety  of  ways 
as  we  experiment  with  more  concrete  contexts.  Determina- 
tion is  thus  a  process  of  rendering  ever  more  concrete  the 
results  produced  by  the  method  of  abstraction. 

Negatively,  then,  determination  deprives  a  given  element 
of  its  splendid  isolation,  and  in  so  doing  usually  deprives 
it  of  part  of  its  clearness  and  simplicity.  But  positively,  by 
fitting  it  into  a  context  which  is  adapted  to  it,  determination 
usually  supplies  the  element  In  question  with  accretions  of 
meaning,  and  the  new  context  may  make  an  enormous  differ- 
ence to  the  signiflcance  of  such  an  element.  For  instance, 
a  system  of  ethics  constructed  in  the  abstract  world  of  pure 
concepts  may  be  very  clear  in  itself,  and  very  explicit  as  to 
our  duty  and  our  highest  good.  We  must,  we  are  told,  aim  at 
so  acting  as  to  treat  others,  not  as  means,  but  as  ends  in 
themselves.  Another  similar  precept  is  to  act  from  pure 
reverence  for  the  moral  law,  or  to  aim  at  loyalty  to  loyalty 
Itself.  In  the  abstract  conceptual  realm — i.  e.,  In  what  Kant 
calls  the  metaphysic  of  ethics — these  ideas  may  be  extremely 
clear.  But  when  we  attempt  to  apply  them  in  more  concrete 
cases,  {.  e.,  to  determine  them  in  reference  to  a  special  con- 
text, they  tend  to  lope  much  of  their  abstract  clearness,  and 
to  become  mixed  up  with  all  kinds  of  interests,  feelings,  and 
Instinctive  desires.  Every  motive-complex  Into  which  they 
enter  endows  them  with  new  shades  of  meaning  until,  in  many 
cases,  it  is  almost  impossible  to  discover  a  trace  of  the 
original  ethical  motive. 

So  far,  we  have  been  considering  determination  purely 
from  the  side  of  the  abstract  element  which  we  seek  to  deter- 
mine. But  we  must  also  consider  it  from  the  side  of  the  con- 
text into  which  wp  seek  to  introduce  the  element  in  question. 
This  context,  in  order  to  admit  of  the  addition  of  such  an 
element,  must  Itself  be  incomplete  and  abstract.  If  the 
element  is  made  more  concrete  by  being  placed  in  the  context, 
the  context  must  be  made  more  concrete  by  the  addition  of 
the  element  In  question.  Determination  is  two-sided  and 
reciprocal.  If  x  is  determined  in  relation  to  o,  ft,  c  .  .  , 
o,  &.  c    .     .     .    ,  are  determined  in  relation  to  «.    Thm, 


\ 


254 


DETKRMINATION 


in  the  case  mentioned  above,  if  the  ethical  motive  is  altered 
by   its   union    with    the   psychological   motives,   psychological 
motives    are    often    transformed    into    something    higher    by 
union   with  ethical   motlves-f .  y..   m  the  case  of  love  i     In 
fact,  such  a  "context"  may   itself  consist  of  not  more  than 
pne   element,   and    may   be   as   isolated   and   abstract   as   the 
element   with   whi.  h   we  start.     In  such  caws  it   is  easy  to 
see  that  both   become  more  concrete   in   their  inter-relation 
and  that  they  determine  each  other.     For  example,  the  con- 
cept of   "Becoming-   arises,   according   to   Hegel,  as  a   recip 
rocal  determination  of  the  two  abstract  concepts  of  "Being" 
and  "Not-being."     Be.oming,  that  is  to  say,  means  the  pas- 
sage from  one  to  the  other,  and  is  the  only  way  in  which  such 
abstract  concepts  can  be  unified  and  given  concrete  meaning. 
One    further    point    remains    to    be    considered.      We    have 
spoken    so    far    as   though    only    "elements"    were   capable   of 
being  determined.     But  we  saw  in  the  case  of  analysis  that 
it  was  possible   to  isolate  not   only   an  element  but  also  an 
aspect  of  a  concrete   situation.     So   too   with   determination 
We  can  determine,  not  only  elements,  but  also  aspects.     We 
may.  for  instance,  start  with  a  general  aspect  or  view  of  a 
person's  character.     This  is  abstract,  for  it  is  divorced  from 
knowledge  of  his  ways  of  acting  in  specific  cases.     We  may 
for  example,  have  heard  in  a  general  sort  of  way,  that  "X  is 
a  good   kind  of  fellow."     If  now  we  are  brought  into  much 
contact  with  X.  it  is  possible  to  determine  further  this  gen- 
eral, vague,  and  abstract  outline  of  his  character,  and  fill  It 
out  with  a  wealth  of  concrete  detail.     We  note  his  behavior 
In  matters  regarding  himself  and  his  self-interest.     We  note 
his  behavior  in  matters  regarding  others,  in  public  as  well 
as   in   private— how   he   meets   his   obligations,   how   he   goes 
beyond   his  strict  obligations  and  likes  to  do  something  for 
the  other  fellow.     In    each   case   we  acquire  a   more  definite 
and   detailed    knowledge   of   his   character,   or— to   express   it 
otherwise— the    vague    Indeterminate    <oncept    "good    kind    of 
fellow"   becomes  thoroughly  determinate  and   clear-cut    After 
a  year's  close  association  with   A",  our  idea  of  his  character 
has  become  very  definite  and  specific. 

Determination,    then,   consists    in    the   synthesi.s   of   two   or 

more  relatively  abstract  elements  or  aspects,  in  the  bringing 

these  in  relation  to  one  another  in  such  a  way  that.  In  virtue 

of  this  relation,  each  takes  on  new  qualities  or  characteristics, 

K'f.  iK-woy  inul  Tufts.  KthUa.  pp.  ZuH  (T. 


AIM  OF  DETERMINATION  255' 

and  becomes  more  spedflo  and  concrete — as  { 1 )  the  moral  law 
becomes  concrete  by  applying  It  to  a  special  case  of  choice, 
and  the  choice  Itself  becomes  ethical  by  our  reference  to  the 
moral  law,  or  (2)  as  our  insight  Into  X'a  character  becomes 
more  concrete  by  studying  his  behavior  in  special  circum- 
stances, and  our  understanding  of  his  behavior  in  special 
circumstances  Is  made  more  profound  because  of  our  gen- 
eral insight  Into  his  character  as  a  whole. 

Aim  of  Oeterminatlon  (A)  Objectivity.— We  determine, 
then,  by  bringing  x  in  relation  to  a,  b,  <  .  .  .  and  noting 
carefully  the  resulting  modifications.  In  so  proceeding  we 
aim.  In  the  first  place,  at  objectivity.  If  i.s  because  we  find 
determination  an  indlspenslble  method  in  dealing  with  the 
objective  world,  that  we  mal<e  use  of  it.  Abstractions  may 
be  correct,  but  we  tend  to  find  them  unsatisfying.  They  seem 
to  belong  to  the  twilight  world  of  mere  theory,  whereas  we 
seelt  the  golden  tree  of  life.  How  many  a  student  of  abstrac- 
tions has  felt,  like  Faust,  that  he  is  getting  out  of  touch 
with  vital  things,  and  must  plunge  into  the  concrete  in  order 
to  recover  his  mental  and  moral  balance?  Mental  models  are 
of  value  only  so  far  as  they  serve  to  bring  lu  into  closer  and 
more  accurate  contact  with  the  objective  world.  We  theorise 
In  order  to  practise,  and  abstract  in  order  to  determine;  and 
what  we  wish  to  determine  is  always  what  we  take  to  be 
what  is  most  real  in  our  experiences.  We  wish  to  under- 
stand reality,  not  only  in  principle,  but  also  in  detail.  In 
the  concrete.  And  the  first  aim  of  determination  is  to  ensure 
that  the  concrete  detail  which  our  methods  bring  to  light 
shall  be  objective,  and  shall  bring  us  into  yet  closer  intimacy 
with  nature  and  ourselves. 

Starting,  then,  as  we  do.  with  elements  or  aspects  which 
are  the  products  of  a  partially  objective  analysis  and  abstrac- 
tion, we  hope  by  comparing  these  one  with  another,  by  turn- 
ing them  over  and  over.  Inspecting  them  from  all  sides  and 
in  all  itinds  of  relatlon.s.  to  arrive  at  a  still  more  objective 
understanding  of  the  world  in  which  we  live. 

(B)  Completeness. — In  the  second  place,  we  aim  at  com- 
pleteness, not  perhaps  in  any  absolute  or  final  sense,  but  at 
least  at  the  greatest  degree  of  completeness  which  can  be 
attained.  We  are  never  satisfied  with  acquiring  one  or  two 
new  determinations  for  our  concepts.  We  wish  our  determ- 
ination to  be  as  complete,  as  many-sided,  and  as  methodical 


?'.^ 


w 


256 


DETERMINATION 


fl^ 


ua 


m 


as  ig  possible.  The  complete  and  final  determination  of  the 
moral  law.  for  Instance,  or  of  a  person's  character,  seems  out 
of  the  question  for  any  understanding  short  of  Omniscience. 
But  we  try  to  fit  the  rule  to  the  case  as  methodically  and  as 
completely  as  the  nature  of  the  case  allows,  and  by  varying 
our  viewpoint  as  much  as  possible,  to  take  Into  consideration 
a  wide  variety  of  possibilities. 

How  Far  Realisable?    (A)    With  IVIind.lVlade  Entitiea.— The 
aim.  then,  of  determination  Is,  by  bringing  x  In  relation  to 
"'''•'■     •     •       -to  discover  new  and  concrete  modifications  of 
x—and  also  of  a,  b,  c     .     .     .—which  are  of  objective  signif- 
icance, and  to  make  our  list  of  such  modifications  as  complete 
as  possible.     How  far  can  this  aim  be  realised?     Let  us  first 
consider  (a«es   from    the  world   of  mind-made   constructions 
An  engineer  who  is  interested  In  inventing  an  air-plane  motor, 
for  example,  has  a  fair  general  idea  of  what  conditions  are 
to  be  met.  and  of  what  type  of  engine  Is  capable  of  meeting 
such  conditions.     But  his  Idea  Is  still  In  part  Indeterminate. 
He  accordingly  studies  a  number  of  models  In  actual  use.  a, 
».  c     .      .      .,  and  by  comparing  closely  his  Ideas  with  a,  per- 
ceives both  excellencies  and  defects  in  that  motor,  in  such  a 
way  that  his  general  Idea  becomes  yet  further  modified,  both 
positively   and    negatively.     He   next   studies   6,  and   obtains 
yet  further  notions  from  that  study.    At  the  end  of  his  study 
of  actual  models,  the  model  he  has  been  shaping  in  his  mind 
has   become   very   sharply   determined,   both   negatively   and 
positively,  and  he  Is  now  prepared  to  make  and  test  a  new 
model  of  his  own.     The  det  rmlnatlons  which  his  Idea  has 
undergone  are  of  some  objective  significance— for  they  have 
been   made  in   relation  to  actual   working  models,  and  with 
express  reference  to  the  conditions  which  should  be  satisfied 
by  an  Ideal  model.     At  the  same  time.  If  his  comparison  in 
the  case  of  each  Individual  model  has  been  exhaustive,  it  is 
possible    for   each   determination   to  be   reasonably  complete, 
and  if.  further,  the  number  of  motor-types  in  actual  existence 
Is  small,  it  Is  possible  for  the  determination  as  a  whole  to  be 
reasonably  complete.     Absolute  finality  In  point  of  objectivity 
and  completeness  Is  hardly  to  be  expected,  as  the  history  of 
invention   shows— for   there  Is  always   room  for  yet  further 
Improvements.    But  In  general.  In  dealing  with  machines  It  is 
possible    for   determination    to   assist    in    producing    marked 
imp  ovement  over    (I)   one's   own  previous  ideas  or  mental 


AIM  OF  DETERMINATION 


2S7 


models,  and  (2)  the  actuallsed  mental  models  of  other  Inven- 
tors.    It  is,  in  short,  possible  to  approach  a  solution  of  the 
objective  problems  rather  better  than  has  been  accomplished 
by  any  Invention  up  to  date.    That  is  to  say,  in  all  such  cases 
determination  can  be  both  objective  and  reasonably  complete. 
Let  us  consider  another  case.    We  all  have  a  certain  vague 
general  idea  as  to  the  nature  of  the  beautiful.    This  general 
idea,  which  is  indeterminate  and  abstract.—^,  e.,  not  in  close 
contact  with  the  world  of  actual  art-creations— we  can  make 
more  determinate  and  concrete,  by  bringing  it  in  relation  to 
actual  concrete  attempts  to  realise  the  idea  of  the  beautiful. 
We  can  study  pictures,  poems,  music,  etc.    That  is  to  say,  we 
can  determine  our  general  idea  by  bringing  it  into  close  con- 
tact with  actual  artworks  and  asking  (1)  how  our  ideal  of 
beauty  applies  to  such  cases,  and  (2)  how  far  such  works  sat- 
isfy our  ideal.    In  this  way  we  gradually  educate  our  artistic 
sense  until,  from   only  knowing  in  more  extreme  examples 
what  we  like  and  what  we  do  not  like,  we  have  developed  a 
thoroughly  concrete  and  determinate  artistic  appreciation  and 
artistic  theory.     Such  a  determinate  theory  is  certainly  (1) 
more  objective  than  the  general  idea  with  which  we  started— 
for  it  has  been  developed  by  the  closest  possible  observation  of 
artistic  models,  and  has  become  modified  by  taking  account  of 
the  various  theories  which  have  enjoyed  a  currency  in  the  his- 
tory of  art.  so  that  it  is  no  longer  a  merely  subjective  imagin- 
ing which  has  fed  only  upon  itself— and  (2)  may  be  reason- 
ably complete,  if  we  have  been  careful  and  exhaustive  In  our 
study  of  each  separate  art-work— though,  taken  as  a  whole.  It 
can  never  be  fully  complete,  for  the  number  of  actual  models 
is  very  great,  while  life  is  short.    But  a  certain  well-rounded- 
ness  of  artistic   insight   can  be  attained.  Just  as  a  certain 
degree  of  completeness  in  respect  of  education  in  general  can 
be  attained.     On  the  whole,  ^hen,  we  can  state  that.  In  the 
case  of  mind-made  entities,  determination  can  be  both  objec- 
tive and  reasonably  complete.    That  is  to  say,  it  can  bring  us 
Into  closer  and  more  complete  contact  with  objective  conditions 
and  objective  facts  than  is  possible  apart  from  such  determi- 
nation. 

(B)  With  Natural  Phenomena.— In  dealing  with  phenomena 
other  than  mind-made  entities,  what  is  our  procedure?  In 
the  cases  from  biology  and  psychology  already  mentioned,  we 
noticed  that  an  abstract  theory  of  muscular  action  or  of  the 


258 


DKTERMINATION 


«>. 


aw>  of  memory  ii  made  determinate  by  being  brought  In  reU- 
tlon  to  a  more  specinc  and  concrete  context.  So  too  the  diag- 
nosing physician  tends  to  have  In  mind  a  general  hypothecs 
as  to  the  nature  of  the  case  which  he  I.  examining,  and  makel 
his  general  hypothesis  more  specific  and  determinate  by  relat- 
^g  It  to  each  symptom  In  turn.  That  Is  to  say.  he  has  in 
mind  a  schematic  and  Indeterminate  mental  model,  which  he 
makes  more  specific  and  definite  by  applying  It.  point  by  point, 
to  the  case  before  him.  How  far  such  procedure  Is  objec- 
tive, depends  partly  upon  the  objective  nature  of  the  preced- 
ing analysis  which  has  divided  the  case  before  him  Into  points 
L'v'^r  w^"'    ^"""°">8  'bis  to  be  partially  objective,  we  can 

t  on  and  bringing  It  In  relation  to  the  other  elements  of  the 
situation  one  at  a  tlme^r  of  taking  a  mental  model  of  the 
whole  and  making  It  more  concrete  and  specific  by  comparlwn 
rhilr^K  !T'°*,  ''"'''^^'^  ^y  *^«  analysls-we  can  My  that 

tlrZTu  f  'r"'  "'  °'^'^"^«  «"  *»>«  •^°«'y-'«  ''hlch  ha. 
preceded  It  and  that.  In  practise.  It  tends  to  be  more  objec- 
tive-*. €.,  to  bring  those  who  use  It  Into  closer  and  more  InU- 
mate  contact  with  the  objective  facts 

be'Vnl?  ?""P'";*"««"'  *  ^'^''^^  at  the  progress  of  science  will 
be  enough  to  show  us  that  completeness  In  any  final  sense  ii 
entirely  out  of  the  question.  For  each  new  generatlo^  ot 
scientists  pushes  further.  Inquiries  which  were  In  many  case, 
regarded  as  sufficient  by  previous  generations.  In  determining 
the  concept  of  arthropod,  for  example,  or  protozoon,  all  that 
can  be  done  Is  to  bring  together  as  carefully  as  possible  all  the 
viewpoints  and  all  the  knowledge  of  the  period,  fnd  thus  bring 

XlTTf   •;  '"""""•  "'^  *°  '"*^-    °"''  *«*»'°°'^«  °'  °atura! 
science   In  fact,  represent  a  kind  of  cross-section  through  the 

[eTand  «n'  tl"?"'"'  °'  '^^  ^"'""^  '°  ^""''"^  *•>«"  «™  writ- 
ten, and  all  that  we  can  ask  of  the  various  determination. 

sZm  h  ""'.'  '^  """""^  °'  *  «'^«°  ^''<^  '•  ^^^tZ 
should  be  up  to  date.     But  the  process  of  scientific  Inquiry 

doe.  not  stand  still,  and  determinations  which  held  good  ten 
years  ago  are  now  out  of  date.  Some  of  them  have  been 
passed  by  In  the  race  for  objectivity,  but  almost  all  are  now 
regarded  as  Incomplete.  Still,  as  In  art  and  education,  so  alM 
in  science.  A  reasonable  degree  of  completenew  can  be 
attained. 

Thus  we  see  that  in  the  case  of  mind-made  entitle.,  and  alM 


VALIDITY  OF  DETERMINATION 


259 


in  the  cmse  of  natural  phenomena,  progreM  In  objective  under- 
sUndlng  U  alwaya  poaalble.  and  a  certain  degree  of  complete- 
neH  can  be  attained,  so  that  the  aim  of  determination  can  In 
both  casea  be  approximately  realised.  In  neither  caae,  how- 
ever, can  it  be  completely  and  finally  realised. 

Validity  of  Determination.— That  some  determinations  are 
fantastic  and  quite  arbitrary.  Is  beyond  reasonable  doubt.  The 
view  of  the  planets  as  a  concrete  system  of  spheres,  set  In 
motion  by  "epicycles'  or  excentrlcs  of  a  crystalline  nature,  la 
determinate,  and  has  even  some  slight  objective  value.  But  as 
a  serious  scientific  explanation  it  has  long  since  been  dla- 
credlted.  The  number  of  epicycles,  in  particular,  which  the 
system  assumed  in  order  to  account  for  the  observed  phe- 
nomena, seems  to  have  been  quite  arbitrary,  and  for  their 
"crystalline"  nature  the  only  evidence  offered  was,  that  they 
must  be  of  some  transparent  substance.  In  order  to  account 
for  their  Invisibility  to  human  eyes.  So  too  the  philosophy  of 
nature  developed  by  the  speculative  philosopher  Schelllng  la 
determinate,  but  is  generally  regarded  as  subjective  and  arbi- 
trary to  the  last  degree.  There  Is,  then,  nothing  sacrosanct 
about  determination  as  such,  and  its  validity  must  accordingly 
be  a  matter  of  how  the  method  is  used.  On  what  condltloni 
la  determination  to  be  regarded  as  valid? 

To  this  question  there  is  only  one  answer  which  we  can 
give.  As  a  scientific  method,  determination  is  valid,  if  and  ao 
far  as  it  brings  us  into  touch  with  objective  laws  and  objec- 
tive facts  in  a  way  which  leads  to  an  advance  in  some  specific 
science.  If  It  "works"—!,  e..  If  it  fits  in  with  the  system  of 
mental  models  approved  by  experience  In  that  particular 
branch  of  inquiry,  and  if  It  also  helps  to  solve  our  particular 
concrete  problem  in  a  satisfactory  manner— so  far  It  can  be 
regarded  as  valid.  But  if  It  is  clear  and  concrete  from  the 
viewpoint  of  intellect  alone,  or  if  imagination  alone.— as  in 
the  case  of  Wolff's  Paychologia  Empirica  or  Schelling's  Natur- 
philoaophie— and  fails  to  bring  us  into  contact  with  the  objec- 
tive world  and  the  realities  of  experience,  It  is  worthless.  How 
far  It  is  valid,  then,  is  a  matter  which  can  only  be  decided  by 
the  grradual  advance  of  science.  There  is  no  easy  and  simple 
criterion. 

Summary.- Determination,  then,  is  a  synthesis  of  x  with  a, 
''.  c  .  .  .  ,  in  such  a  way  that,  as  thus  interrelated,  both 
X  and  a,  b,  (•    .    .     .    take  on  new  shades  of  Hignificance  and 


260 


DETERMINATION' 


become  more  apeciflo  and  concrete.  The  aim  of  determinatioD 
la  to  be  objective  and  reaaonably  complete,  that  la.  to  add  to 
our  Insight  Into  objective  lawa  and  facta  In  a  way  which  can 
be  arcomplUhed  by  no  other  method.  In  the  raae  of  mental 
modela  and  of  natural  phenomena  this  aim  can.  to  a  reason- 
able extent,  be  realised.  But  the  extent  to  which  It  can  be 
realised,  and  In  general  the  validity  of  our  use  of  the  method 
Is  a  matter  only  to  be  decided  In  the  light  of  scientific  prog- 
ress. So  far  as  determination  leads  to  Insight  Into  objective 
structures,  and  helps  us  to  solve  our  concrete  problems  and 
thus  advance  the  8<  lence  into  whose  department  the  problems 
In  question  fall.  Its  use  as  a  scientific  method  Is  Justified. 

Abstraction    and    Determination.— It    remains    to    consider 
briefly  the  relation  of  abstraction  to  determination.     Appar- 
ently, abstraction  Is  analytical  rather  than  synthetical,  while 
determination  Is  synthetical  rather  than  analytical.    Abstrac- 
tion takes  an  element  or  aspect  out  of  Its  concrete  context 
\  Determination  puts  an  element  or  aspect  Into  a  concrete  con- 
text.   Abstraction  and  determination  thus  appear  different  In 
starting-point.  In  result,  and  In  method.    But.  remembering  aa 
we  do  that  analysis  and  synthesis  were  found  to  Involve  each 
other,  and  to  be  two  sides  of  a  single  method,  we  must  ask 
whether  abstraction  does  not  similarly  Involve  determination 
and  determination  Involve  abstraction,  so  that  here  also,  per- 
haps, we  are  dealing  with  two  sides  of  a  single  method. 

Does  Abstraction  involve  Determination?— Let  us  begin  by 
asking  whether  abstraction,  as  such.  Involves  -letermlnatlon 
as  an  essential  part  of  Its  method.     In  abstraction,  we  take 
an  element  out  of  Its  context.    Does  our  procedure,  however 
render    It   absolutely    contextless?     I^t    us   consider.      If   we 
deprived  an  element  of  all  context— of  all  connection  with 
and  Llatlon  to  other  elements— would  It  not  be  cut  off  from 
the   intelligible   world   and   become   meaningless?     It   looks 
then,  as  thonsh  in  taking  it  out  of  context  a  we  are  perhaps 
putting  It  into  context  b;  and  a  little  consideration  will  con- 
vince iia  that  this  is  precisely  what  we  are.  in  fact,  doing 
We  are  alway.s  placlnR  it.  at  least.  In  a  universe  of  meaning 
In  a  system  of  thouRht  which  is  intelligible.    There  is  a  world 
of  concrete  realities,  and  there  Is  a  world  of  abstract  mean- 
ings, and  abstraction  consists  larsely  In  taking  an  element 
out  of  Its  place  in  a  particular  concrete  Hituatlon.  and  giving 
it  a  different  place  In  the  world  of  meanings.    For  example 


ABSTRACTION  AND  Df:TF:RMI NATION  261 

th«  aosicttudcnt  i«ol«tf>i  •  jwlnt  of  technique  for  study  by 
practUIng  It  In  «  context  composed  of  flngerexen aies.  He 
ceaaea  to  play  a  certain  pasHage  In  Llaat  or  Chopin  until  he 
haa  practised  that  kind  of  paaaage  in  Its  contexts  In  the 
flncer-studles  of  Ciemy  or  Hanon.  The  psycholotiat  Isolates 
the  "rote"  element  for  special  study  of  memory-factors  by 
using  the  artiflcial  context  of  nonaense-syllables.  That  is, 
in  fact,  how  we  Isoiatp.  We  extract  the  "rote"  element  by 
using  nonsense-syllables.  We  manage  to  extract  the  "double- 
sixths"  el^nient  by  playing  the  specialised  studies  in  Csemy. 
So  too  with  generalisations.  When  we  generalise,  we  very 
evidently  leave  the  world  of  concrete  fact  and  enter  the 
world  of  mental  models,  the  world  of  sclcntlflc  hypotheses  and 
laws.  In  this  way,  then,  we  see  that  abstraction  involves  deter- 
mination, and  involves  it  as  an  integral  part  of  lU  method. 
Abstraction  from  the  roncrete  Is  at  the  same  time  determina- 
tion in  terms  of  mental  models,  and  it  is.  in  fact,  by  determin- 
ing In  terms  of  mental  models  that  we  manage  to  abstract 
from  the  concrete. 

Doea  Determination  Involve  Abstraction 7— Let  us  now 
reverse  our  Inquiry,  and  ask  whether  determination  aa  such 
Involves  abstraction  as  an  Integral  portion  of  its  method.  If 
we  consider  the  question  closely,  we  see  that  we  are  not  tak- 
ing an  entity  which  is  devoid  of  context,  but  rather  an  entity 
which  belongs  at  least  to  the  world  of  Intelligible  meanings, 
In  order  to  give  it  a  context  which  shall  be  concrete  rather 
than  abstract.  That  is  to  say,  we  abstract  it.  not  from  a  pure 
isolation,  but  from  Its  meaning-context  in  order  to  determine 
It  in  a  more  sensory  context.  As  we  saw.  an  element.  In 
becoming  determinate,  tends  to  lose  something.  The  moral  law 
loses  much  of  the  clearness  and  sharpness  of  outline  which 
belongs  to  It  in  the  metaphysical-ethical  world  of  pure  mean- 
ings, and  takes  on  something  of  the  confusion  and  irregularity 
of  our  psychological  impulses.  Our  psychological  Impulses,  on 
the  other  hand,  lose  much  of  the'r  merely  mechanical  nature 
In  becoming  transformed  Into  something  ethical.  So  too  our 
notion  of  X*«  character  loses  Its  generality  and  schematic 
nature  In  becoming  specific,  and  our  understanding  of  Z'« 
specific  acts  loses  much  of  Its  narrowness  when  envisaged 
from  the  general  standpoint  of  Insight  into  X**  character  aa  a 
whole.  It  is  plain,  then,  that  determination  involves  abstrac- 
tion as  an  Integral  part  of  its  method,  and  that  abstraction 


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262 


DKTERMINATION 


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and  determination  must  accordingly  be  regarded,  not  as  two 
methods,  but  as  two  one-sided  aspects  of  a  single  method. 

Comparison  With  Analysis  and  Synthesis.— What  Is  the  rela- 
tion of  this  method  to  the  analytic-synthetic  method?  In  the 
first  place,  it  is  a  less  elementary  method.  It  presupposes 
both  analysis  and  synthesis,  and  starts,  not  with  a  concrete 
situation,  but  with  a  context  already  analysed  out  into  ele- 
ments, or  with  elements  already  analysed  out  of  a  context. 
In  the  second  place,  It  takes  us  further  in  our  investigation  of 
objective  laws  and  facts.  By  taking  one  thing  at  a  time  and 
concentrating  our  whole  powers  in  a  single  direction,  we  are 
able  gradually  to  make  further  progress  than  would  otherwise 
be  possible.  As  a  scientific  method  whose  aim  58  to  place  us 
in  toi'ch  with  the  objective  world,  abstraction  and  determina- 
tion represent  a  considerable  advance  upon  analysis  and  syn- 
thesis, a  carrying  further  of  the  work  which  the  more  pre- 
liminary method  had  begun. 


FOB  FURTHER   READING 

B.  Bosanquct,  Logic,  Vol.  II,  pp  168-172.  Chr.  Slgwapt,  Logk,  Vol. 
I,  pp.  20ri-270.     W.  W'Tindt.  Logik,   (3rd   Edit.),  Vol.   II,  pp.  17-19. 

EXERCISES 

Show  what  part  Is  played  by  determination  In  dealing  with  the 
following  cases :  ( 1 )  In  looking  up  the  meaning  of  a  word  In  the 
dictionary.  (2)  In  selecting  courses  of  study  In  one's  junior  yeur  in 
college.  (3)  In  ascertaining  the  grounds  for  a  gloomy,  depresi^ed 
feeling.  (4)  In  choosing  pictures  for  one's  room.  (5)  In  choosing 
one's  friends.     (6)   In  wrlttag  a  "report"  on  an  assigned  book. 


;{:',. 


5' 


CHAPTER  XXIV 

INDUCTION 

Nature  of  Induction.— Induction  is  a  highly  complex  method 
of  scientific  investigation.    It  makes  use  of  analysis  and  syn- 
thesis, abstraction  and  determination,  in  all  their  varieties  and 
in  any  order  which  suits  its  problems.    What  holds  together 
this  use  of  these  various  methods  and  gives  to  induction  an 
existence  in  its  own  right,  and  specific  significance  as  one  of 
the  most   Important   of  the   scientific   methods,  is   Its  goal. 
Analysis  takes  apart,  abstraction  isolates  or  generalises,  but 
induction  discovers  laws.    It  is  this  which  distinguishes  induc- 
tion from  abstraction  and  determination,  which  are  concerned 
with  concepts  rather  than  with  laws,  though  they  also  estab- 
lish certain  empirical  generalisations.    It  is  this  also  which 
marks  its  importance  for  science.    Analysis  and  synthesis  are 
more  preliminary,  and  deal  more  with  concrete  situations. 
Abstraction  and  determination  are  more  advanced,  and  carry 
further  the  work  started  by  analysis  and  synthesis.    But  Induc- 
tion—and deduction— are  the  most  advanced  of  all  the  scien- 
tific methods,  and  carry  to  its  full  completion  the  work  of 
these  preliminary  methods.    The  chief  aim  of  investigation  is 
the  discovery  of  laws,  and  induction  thus  sums  up  all  the  other 
methods  in  itself,  and  carries  their  work  to  its  completion,  so 
far  as  this  is  possible.    The  nature  of  induction,  then,  is  to 
discover  laws. 

I. How  is  this  done?    There  are  two  main  ways,  which  at 

first  sight  seem  sharply  distinct.  In  the  first  place,  we  have 
the  kind  of  generalisation  which  we  have  already  studied 
under  the  name  of  abstraction.  In  inducfton  this  method  Is 
largely  used,  but  is  carried  a  little  further.  By  taking  a 
variety  of  instances  of  the  problem  under  investigation,  it  is 
possible,  if  we  compare  them  carefully  in  respect  of  all  the 
points  already  made  clear  by  analysis,  to  eliminate  a  large 
number  as  immaterial,  and  thus  to  narrow  the  field  to  such  an 
extent  that  an  explanation  in  terms  of  some  working  hypothe- 
sis is  more  easy  to  discover.    Similarly,  by  taking  both  posl- 


263 


264 


INDUCTION 


I' 


hi 

i ; 
I 


tive  and  negative  instances — that  is  to  say,  (1)  instances  in 
which  the  particulai  point  in  which  we  are  interested  is  pres- 
ent, and  (2)  instances  closely  resembling  the  former,  but  dif- 
fering in  that  the  point  in  question  is  absent — it  is  possible, 
by  a  careful  comparison,  to  eliminate  a  great  deal  which  is 
immaterial,  and  thus  considerably  to  simplify  our  problem. 

For  example,  if  a  large  number  of  cases  of  ptomaine  poison- 
ing are  reported  from  a  single  district,  it  is  possible,  by  care- 
ful comparison  of  the  chief  circumstances  revealed  by  the  pre- 
liminary analysis,  to  eliminate  points  which  vary  in  the  vari- 
ous cases,  and  to  narrow  the  problem  to  a  consideration  of 
the  points  which  remain  constant  throughout  the  whole  series 
of  cases.  U  A,  B,  and  C  were  at  work  on  drains,  while  D,  E, 
F  .  .  .  were  not  and  yet  were  poisoned,  the  drains  as  a 
possible  factor  can  as  a  rule  be  eliminated.  Similarly  if  A,  B, 
and  C  were  poisoned,  while  II,  i,  J  .  .  .  were  also  at  work 
on  the  drains  but  were  not  poisoned — this  is  a  negative 
instance — the  drains  as  a  factor  to  be  considered  would  prob- 
ably be  eliminated,  at  least  provisionally.  As  a  rule  a  prob- 
lem of  this  kind  becomes  narrowed  down  to  such  a  point  that 
it  is  discovered  that  all  were  taken  ill  after  their  evening 
meal,  and  that  the  materials  for  the  evening  meal  were  almost 
all  purchased  at  a  single  store.  It  is  then  possible  to  carry 
on  the  same  method  of  elimination  of  variables  until  only  the 
elements  common  to  every  meal  are  left — such  as  canned  food 
and  one  or  two  other  items.i  When  the  problem  is  thus  nar- 
rowed down,  a  hypothesis  at  once  suggests  itself,  and  leads  to 
the  immediate  impounding  of  samples  of  the  food  in  question 
for  purposes  of  chemical  analysis. 

So  too  in  the  famous  case  of  Sir  Isaac  Newton's  experi- 
ments2  to  discover  the  conditions  on  which  the  colors  of  the 
solar  spectrum  depend.  Newton  so  narrowed  the  problem 
that  he  was  able  to  use  positive  and  negative  instances  which 
were  already  considerably  simplified.  A  ray  of  sunlight 
entered  the  dark  r*oom  of  his  physical  laboratory,  and  shone 
upon  a  screen,  making  a  whitish  or  yellowish  circle  of  light. 
The  spectral  colors  not  being  present,  this  furnished  a  nega- 
tive instance.     By  inserting  a  glass  prism  into  the  path  of 


1  Such  rases  arp  only  ton  common.  In  tlip  particular  case  which 
came  iind^r  rhc  writer's  n.itUc  in  I'.criin  in  IDli! — the  (uusa  mali  was 
German  sausage. 

2  A  careful  discussion  of  the  Inductive  methods  Involved  will  be 
found  In  S.  U.  Melloue's  Loijic. 


NATURE  OF  INDUCTION 


265 


the  ray,  Newton  was  able  to  produce  the  colors  upon  the 
screen.  This  furnished  a  positive  instance.  The  production 
of  spectral  colors  from  the  ray  of  sunlight  was  thus  due  to 
something  in  the  nature  of  the  glass  prism.  Analysis  showed 
that  prisms  might  vary  in  size,  in  shape,  and  in  material. 
Abstraction  suggested  devising  special  experiments  to  test 
each  one  of  these  special  possibilities,  both  positively  and  neg- 
atively. In  these  experiments,  size  was  totally  eliminated, 
material  was  partly  eliminated,  and  certain  kinds  of  shape 
were  eliminated,  other  kinds  being  thus  made  more  deter- 
minate. The  ;>roblem  being  thus  narrowed  down,  the  hypothe- 
sis of  the  composite  character  of  sunlight  suggested  iUelf, 
and  was  subsequently  verified. 

II.— In  the  second  place,  we  have  a  method  which  seems 
more  akin  to  determination.     We  frame  a  possible  explana- 
tion of  the  case  before  us,  and  then  proceed  to  modify  or  deter- 
mine this  hypothesis  by  bringing  it  into  connection  with  the 
points  revealed  by  analysis,  one  by  one.    What  is  superfluous 
or  erroneous  in  the  hypothesis  or  mental  model  becomes  elimi- 
nated and  corrected,  until  finally  it  fits  the  facts  as  closely  as 
we  can  make  it.    For  example,  in  the  work  of  criminal  inves- 
tigation, a  detective  constructs  a  hypothesis  to  account  for  the 
facts,  and  proceeds  to  determine  it  further  by  following  up 
specific  clues,  until  a  satisfactory  conclusion  is  reached.    So 
too  in  prospecting  for  minerals,  it  is  usual  to  start  with  a 
general  hypothesis  based  partly  on  general  mineralogical  infor- 
mation, partly  on  special  local  knowledge,  and  to  determine 
this  hypothesis  by  testing  for  ore  here  and  there  until  a  com- 
pletely satisfactory  conclusion  is  reached.    More  particularly, 
the  method  consists  in  framing  a  hypothesis,  and  then  deduc- 
ing from  the  nature  of  the  hypothesis  or  mental  model  certain 
specific  consequences,  which  can  be  brought  into  more  imme- 
diate relation  to  the  facts  of  the  case.    If  these  do  not  fit  the 
facts,   the  hypothesis   is   modified   until  the   deduced  conse- 
quences and  the  observed  facts  more  nearly  coincide.    This  is 
brought  out  with  especial  clearness  in  Huxley's  marshalling 
of  the  evidence  for  the  evolution  hypothesis.    He  first  deduced 
what,  assuming  the  hypothesis  to  be  correct,  one  would  expect 
the  facts  to  be  in  a  specific  case— the  case  being  concerning 
certain  anatomical  details  to  be  expected  in  the  ancestors  of 
the  horse— and  then  showed  that  the  actual  examples  dis- 
covered and  placed  in  the  Yale  museum  agreed  with  the  deduc- 


266 


INDUCTION 


)| 


tlons  In  question.  He  even  proceeded  to  make  further  prophe- 
cies in  the  shape  of  deductions  along  the  same  general  lines, 
and  these  deductions  have  been  verified  by  more  recent  dis- 
coveries.s 

This  second  method  of  induction,  which  proceeds  by  framing 
mental  models  and  then  determining  these,  does  not  seriously 
differ,  when  we  come  to  look  closely  at  both,  from  the  method 
of  generalising  by  means  of  abstraction.  In  the  first  place, 
they  look  like  two  phases  or  halves  of  one  and  the  same 
method.  Thus,  when  the  problem  of  poisoning  had  been  sim- 
plified to  a  certain  extent,  the  subsequent  procedure  consisted 
in  framing  a  hypothesis  about  the  canned  food,  and  then  deter^ 
mining  this  further  by  means  of  chemical  analysis.  So  too  in 
the  case  of  Newton's  experiment — the  hypothesis  of  the  com- 
posite nature  of  sunlight  was  suggested  after  the  problem  had 
been  partially  simplified,  and  was  subsequently  further  deter- 
mined. That  is  to  say,  it  looks  as  though  the  method  of  induc- 
tion consisted  of  approximately  three  phases: — (1)  analysis 
and  simplification  of  the  problem,  (2)  construction  of  some 
hypothesis  on  the  basis  of  the  simplifying  analysis,  and  (3) 
determination  of  the  mental  model  thus  suggested,  by  careful 
comparison  with  the  facts.  This  last  stage  is  sometimes 
known  as  Verification. 

But,  in  the  second  place,  it  is  possible  to  look  into  the  pro- 
cedure still  more  closely,  and  to  realise  that  it  is  less  with 
two  successive  phases,  and  more  with  two  simultaneous 
aspects,  of  the  inductive  method,  that  we  have  to  do.  The 
method  of  abstraction  and  generalisation,  which  results  in 
eliminating  certain  factors,  really  proceeds  itself  by  the  help 
of  mental  models,  and  thus  may  reasonably  be  regarded  as 
itself  a  determination  of  some  general  hypothesis,  or  making 
it  more  specific.  In  the  poison  case,  the  general  hypothesis 
concerns  the  source  of  the  poison,  and  this  hypothesis  cer- 
tainly is  present  in  the  beginning  and  becomes  determined 
and  narrowed  down  with  each  step  in  the  inquiry.  In  fact, 
the  whole  problem  may  reasonably  be  regarded  as  an  attempt 
to  determine  the  source  of  the  poison.  So  too  Newton  had  a 
general  idea  that  there  must  be  something  in  the  nature  of 
sunlight  which  made  it  possible  for  the  spectral  colors  to  be 

sSee  Huxley's  lecture.  The  DcmonntraHve  Evidence  of  Evolution 
It  1«  quoted,  with  a  few  omissions.  l)y  A.  L.  Jones,  Loyic,  inilucUve 
mill  deilm-tti-e,  pp.  287-riOO. 


AIM  OF  INDUCTION 


267 


produced  in  his  experimental  laboratory,  and  each  step  in  the 
experiment  may  legitimately  be  regarded  as  making  this  gen- 
eral idea  or  hypothesis  more  determinate  and  specific.  So  too, 
on  the  other  hand,  by  following  up  special  clues,  the  detective 
is  learning  what  may  be  eliminated,  and  by  his  special  tests 
the  prospector  is  discovering  what  sites  may  be  regarded  as 
unpromising  and  negligible.  There  is  thus  one  complex 
method,  which  results  in  the  discovery  of  some  principle  or 

law. 

Aim  of  Induction    (A)    Objectivity.— Induction,  then,  is  a 
highly  complex  method,  which  employs  all  the  resources  of 
analysis  and  synthesis,  of  abstraction  and  determination,  until 
our  mental  models  approximately  fit  the  facts  under  consid- 
eration,  and  we  are  thus  able  to  discover  some  principle  or 
law.    The  aim  of  induction  is,  first  and  foremost,  to  be  objec- 
tive.   We  do  not  wish  to  discover  some  hypothesis  which  sat- 
isfies us,  but  turns  out  to  be  fatastic  or  unverifiable,  when 
brought  Into  connection  with  the  actual  facts.     We  seek  to 
discover  objective  laws,  laws  which  really  seem  to  apply  to 
the  factb.    Sometimes  It  is  in  terms  of  causal  models,  some- 
times in  terms  of  mathematical  models,  sometimes  In  terms 
of  models  which  belong  to  a  more  specific  branch  of  scientific 
Inquiry,  as  when  we  seek  to  discover  the  principle  which  holds 
a  particular  botanical  theory  together,  or  which  unifies  the 
various  ways  in  which  a  particular  term  is  used  in  literature. 
The  use  of  the  various  scientific  methods  in  order  to  discover 
a  principle  or  law  which  is  of  objective  significance,  is  the 
primary  aim  of  induction,  whether  the  principle  is  causal, 
mathematical,  or  what  not. 

(E)  Completeness. — In  the  second  place,  induction  aims  at 
completeness.  As  we  saw,  the  characteristic  which  distin 
guishes  induction  from  the  methods  previously  considered,  is 
that  it  carries  their  investigation  further.  That  is  to  say,  it 
aims,  not  only  at  a  greater  degree  of  objectivity,  but  also  at  a 
greater  completeness  of  investigation.  Abstraction  Is  satisfied 
with  isolating  some  special  element  or  aspect.  Determination 
is  satisfied  with  making  some  such  element  or  aspect  concrete 
and  specific.  Induction  aims  at  carrying  the  investigation 
further,  and  abstracting  or  determining  the  law  which  governs 
the  case  in  question — and  at  discovering  it  as  completely  as 
may  be  possible.  It  is  usually  thought  that  induction  is  never 
perfectly  complete,  and  that  science  aims  at  progressivenesa 


; 


^r-A^  ^.'Aak-^ 


268 


INDUCTION 


li! 


I 


and  frultfulness  In  Its  solutions,  rather  than  at  formulations 
which  are  to  be  accepted  as  final.  But  there  can  be  no  doubt 
that  it  Is  satisfied  with  nothing  less  than  the  fullest  determi- 
iiatlon  of  which  the  evidence  admits.  Objectivity,  then,  and 
completeness  represent  our  aim  in  using  the  method  of  induc- 
Uon. 

How  Far  Realisable?  (A)  With  Mind  Made  Entitles.— Give 
a  college  graduate  one  of  the  psychological  puzzle-boxes,  and 
ask  him  to  find  out  the  principle  in  accordance  with  which  it 
can  be  opened  and  shut.  For  convenience  of  reference,  let  us 
consider  the  box  to  which  we  previously  referred.*  A  little 
experimenting  completes  the  work  of  analysis  and  synthesis. 
The  factors  are  learnt  to  be  (1)  the  two  levers,  (2)  the  bolt 
which  falls  by  its  own  weight  when  both  levers  are  drawn  out 
and  the  box  is  placed  upon  the  white  side,  and  (3)  the  com- 
bination lock.  Abstraction  and  determination  further  are 
brought  to  bear  upon  (1)  and  (2).  until  the  principle  which 
governs  them  is  discovered.  Then  the  combination  lock  is 
experimented  with,  in  terms  of  one  mental  model  after 
another,  until  the  limits  within  which  it  works  are  finally 
determined.  These  items  of  knowledge  thus  ascertained,  their 
application,  in  the  proper  order,  to  the  different  elements  of 
which  the  works  of  the  box  are  composed,  will  open  the  door. 
^The  student  is  now  possessed  of  the  principle.  His  Induction 
:  is  certainly  objective,  for  it  works.  He  can  actually  open  the 
box  before  him.  He  understands  the  principle  of  the  thing. 
His  insight  can  reasonably  be  regarded  as  complete.  For  what 
remains  to  be  discovered?  Once  the  box  is  opened,  the  struc- 
ture, at  which  he  had  previously  guessed,  becomes  visible,  and 
even  the  combination  lock  can  be  taken  to  pieces  without  much 
difficulty.  It  is  true  that  certain  ultimate  problems  in  physical 
science— e.  g.,  as  to  the  nature  of  levers,  including  the  ques- 
tion why  one  end  should  move  when  we  move  the  others 

remain  unsolved.  But  those  go  beyond  his  problem.  His 
problem  was  to  open  the  box,  and  to  find  out  the  principle  of 
its  works.  He  has  opened  the  box,  and  has  found  out  the 
principle.  His  problem  is  solved,  and  his  induction  can  thus 
be  regarded  as  not  only  objective,  but  also  complete. 

Let  us  consider  another  example.     In  working  out  a  text- 


*  Cf.  p.  221  above. 

»  Cf.  Sir  Oliver  Lodge,  The  Survival  of  Man,  p.  81. 


AIM  OF  INDUCTION 


269 


*  ook  problem  in  oimultaneous  quadratics,  the  first  tblDg  to  do 
is  to  get  the  conditions  stated  in  terms  of  xi  and  y^.    This 
represents  the  work  done  by  analysis  and  synthesis,  and  in 
the  case  of  most  text-book  examples  is  practically  done  for  us. 
Then  follows  the  work  of  abstraction  and  elimination,  and 
this  complex  procedure  is  continued  until  eventually  we  have 
eliminated  everything  on  one  side  of  our  equation  but  x,  and 
on  the  other  side  everything  but  a  numerical  value — say  5. 
We  then  go  back  to  our  first  mental  model,  e.  g.,  an  equation 
of  the  form  2x2 — J,xv+y'i=50  and,  by  substituting  for  x  Its 
numerical  value  5,  are  able  to  eliminate  x  and  thus  determine 
y,  eventually  discovering  that  y=20.     In  this  way  we  have 
discovered  the  principle  or  law  which  we  were  seeking.    The 
result  is  objective,  for  it  Is  obtained  by  rigorous  operations 
upon  the  analytic-synthetic  reconstruction  of  the  data.    It  is 
also  complete,  for  the  problem  is  solved.    It  Is  true  that  the 
solution  of  equations  presupposes  answers  to  a  number  of 
mathematical,  logical,  and  even  metaphysical  questionings,  but 
these  lead  beyond  the  problem  with  which  we  were  dealing. 
That  has  been  definitely  solved.    If  such  cases  are  to  be  con- 
sidered as  typical,  we  can  say  that  in  the  case  of  mind-made 
entities,  where  thought  Is  dealing  with  itself  and  Its  own  con- 
structions, our  Inductions  can  be  both  objective  and  complete. 
(B)  With  Natural  Phenomena. — In  cases  where  thought  has 
to  deal  with  phenomena  other  than  its  own  constructions,  the 
path  to  objectivity  and  completeness  does  not  seem  so  certain. 
We  proceed,  by  constructing  mental  models,  and  by  a  process 
of  trial  and  error  which  eliminates  the  less  promising  of  these, 
to  simplify  our  problem  In  various  ways,  using  analysis  and 
synthesis,  abstraction  and  determination,  until  In  the  end  we 
have  brought  our  mental  model  as  close  to  the  objective  laws 
and  facts  as  seems  In  our  power,  and  have  made  It  as  com- 
plete as  we  can.    There  Is,  however,  as  we  have  seen  before, 
always  some  gap  between  our  mental  models  and  the  empirical 
facts.    For  Instance,  In  using  the  mathematical  typo  of  model, 
we  might  even  use  one  In  the  form  of  simultaneous  quadratic 
equations — thus  to  some  extent  resembling  the  mind-made  case 
mentioned  above.    Once  our  data  are  expressed  In  algebraical 
form,  a  conclusion  can  be  worked  out  which  Is  both  objective 
and  complete  so  far  as  the  mathematical  conditions  are  con- 
cemed.    But  between  a  given  school-book  example  and  a  real 
problem  In  physical  science,  there  Is  all  the  difference  In  the 


270 


INDUCTION 


m 


•«} 


i 


world.     The  school-book  example  la  mind-made,  and  can  be 
fitted  completely  and  without  remainder  into  the  equational 
form  In  question.    But  the  phenomena  dealt  with  in  physical 
science  are  seldom,  If  ever,  of  this  exact  form.     There  is  In 
practise  always  a  certain  marginal  error,  and  our  examples, 
as  a  rule,  refuse  to  work  out  nicely.     We  cannot  quite  over- 
come the  gap  which  separates  our  models  from  the  phenomena 
which  we  are  studying,  though  we  tan,  by  improved  methods 
of  determination,  reduce  this  gap  to  very  small  proportions. 
In  the  case  of  the  poisoned  workmen,  for  instance,  the  methods 
employed  rarely  prove  in  a  way  which  could  be  regarded  as 
completely  satisfactory  that  the  poison  came  from  the  canned 
food.    We  need  the  further  chemical  analysis,  and  till  that  has 
been  performed,   we  tend   to  suspend  judgment.     Even  the 
chemical  analysis  is  not  perfectly  satisfactory.    So  too  in  crim- 
inal cases,  circumstantial  evidence  may  point  strongly  in  one 
direction,  and  may  still  be  entirely  misleading,     in  fact.  In 
dealing  with  such  phenomena,  our  methods  seem  to  be  like 
those  of  Indirect  proof,  where  direct  insight  is  not  to  be  had. 
Inductive  methods.  In  such  cases,  seem  like  an  attempt  to  sub- 
stitute painstaking  completeness  for  direct  insight.     We  try, 
by  proceeding  both  positively  and  negatively,  so  to  manipu- 
late the  analysed  data,  that  one  mental  model  seems  highly 
probable  and  all  alternative  explanations  which  could  reason- 
ably  be  framed   are  shown   to  be   Improbable,  and  are  thus 
eliminated.     But  nothing  short  of  direct  insight  is  perfectly 
satisfactory,  and  In  dealing  with  natural  phenomena  we  have 
put  up  with  something  short  of  direct  Insight,  and  can  thus 
only  approximate  to  realising  the  aim  of  objectivity  and  com- 
pleteness. 

Types  of  inductive  Method.— The  chief  types  of  inductive 
method  are  the  mathematical  and  the  causal.  That  is  to  say, 
we  can  distinguish  Inductive  types  in  terms  of  the  type  of 
mental  model  employed.  In  practise,  however,  these  re:>re- 
sent  only  the  two  chief  forms.  Strictly  speaking,  there  are  at 
least  as  many  tyi)es  of  inductive  method  as  there  are  specif- 
ically distinct  sciences,  and  as  these  are  not  only  indefinite, 
but  also  Increasing  in  number,  it  seems  unprofitable  to  attempt 
In  any  way  to  sum  them  up.  Attempts  have  been  made  to  dis- 
tinguish inductive  methods  according  as  positive  instances 
alone  are  employed,  or  a  mixture  of  positive  and  negative 
Instances,  etc.,  but  in  practise  all  instances  are  partly  positive 


VALIDITY  OF  INDUCTION 


271 


and  partly  negative,*  so  that  It  is  unwise  to  attempt  to  intro- 
duce distinctions  whicli  are  without  practical— i.  e.,  objective 
— significance.  The  only  safe  statement  for  us  to  make  is, 
that  induction  is  a  highly  complex  method  of  scientific  inves- 
tigation, which  feels  its  way  by  means  of  analysis  and  lyn- 
thesis,  abstraction  and  determination,  until  it  reaches  some 
approximation  to  insight  into  the  law  for  which  it  is  seeking. 

Validity  of  Induction.— In  dealing  with  mental  structures — 
i.  e.,  with  cases  in  which  it  is  possible  to  attain  to  an  insight 
which  is  both  objective  and  complete — it  is  easy  to  test  the 
validity  of  an  induction.  An  induction  is  valid  which  really 
leads  to  such  insight.  When  we  have  reached  the  principle 
which  makes  clear  the  fastening  of  our  puzzle-box,  or  the  solu- 
tion of  the  problem  in  simultaneous  quadratics,  we  know  that 
our  induction  has  been  valid,  because  it  works  in  a  way  which 
we  can  test  directly,  and  can  understand.  But  in  dealing  with 
natural  phenomena,  where  such  direct  insight  is  out  of  our 
power,  our  inductions  can  only  approximate  to  full  validity. 
In  such  cases,  we  can  say  that  they  are  valid  so  far  as  they 
work — i.  e.,  so  far  as  they  enable  us  to  understand  the  law  in 
question.  For  example,  if  we  can  predict,  from  our  approxi- 
mate insight  into  some  such  law,  what  will  happen  in  a  given 
case,  and  experience  really  fulfllla  our  prediction, — if  we  can 
handle  phenomena  much  as  though  they  were  mental  models — 
as  we  seem  able  to  do  in  calculating  eclipses — so  far  we  can 
regard  our  inductions  as  valid.  But  for  approximation  to  a 
progressively  more  objective  and  more  complete  insight  into 
the  structure  of  natural  law,  we  must  look  to  indefinitely  con- 
tinued inductive  inquiries — i.  e.,  to  the  development  of  empir- 
ical science  itself.  It  is  only  in  the  light  of  wider  and  deeper 
knowledge  that  we  can  Judge  whether  our  present  experiments 
are  leading  in  the  right  direction  or  not.  The  "right"  direc- 
tion is  the  one  which  leads  to  a  more  objective  and  more  com- 
plete knowledge  of  the  laws  which  seem  to  underlie  natural 
phenomena. 

Summary.— Induction  is  a  complex  method  of  investigation 
which  sums  up  in  itself  the  work  of  analysis  and  synthesis, 
abstraction  and  determination,  and  carries  this  work  further, 
until  It  discovers  Botne  law.     Its  aim  Is  objectivity  and  com- 

»For  example,  the  "positive"  inetances  agrree  In  the  presence  of 
the  phenomenon  In  question  but  disagree  by  varying  In  many  other 
respects.  That  Is  to  say.  In  respect  of  points  other  than  the  phenom- 
enon In  question,  such  Instances  ai-e  "negative." 


272 


INDUCTION 


I- ' 


pletenesa,  and  this  aim  can  be  realised  with  mental  atructurei, 
but  not  precisely  with  natural  phenomena.  The  Talidlty  of 
Induction  is  tested  by  inquiring  bow  it  "works,"  and  can  thus 
be  settled  only  by  more  prolonged  experimentation,  i.  e.,  by  the 
progress  of  science  itself. 


11 


rOR  PURTHRR  RRADINO 

B.  BoMnquet,  Lof/ic,  Vol.  II.  pp.  175-170.  F.  II.  lipsdley.  PHnciplf 
of  Logic,  pp.  320-342.  B.  Erdmann,  Logik,  (2nd  Wit.),  pp.  742-754, 
774-784.  II.  AV.  B.  JoRppb,  IntroducHon  to  Logic,  chaptprs  itI!I-zIi. 
Chr.  SiKwart.  Logic.  Vol.  II,  pp.  288-311.  W.  Wundt,  Logik  (Srd 
Kdlt.).  Vol.  II,  pp.  20-30. 


i 


BXERCISE8 

IIow  mlfrht  the  following  casea  be  InvestlKated  Inductively:  (1) 
The  theft  of  a  sum  of  money  from  a  room  In  a  hoRpltal  to  which 
only  three  nurHes  have  acteaa.  (2)  The  romitaratlve  teaching  efficiency 
of  three  grade  school  teachers.  (3)  The  meaning  of  "Imagination" 
In  Aristotelian  psychology.  (4)  The  comparative  efficiency  of  party 
government  and  non-partisan  government.  (5)  The  degree  of  accuracy 
with  which  we  can  localise  touches  on  the  forearm.  (6)  The  etTect 
of  wave-action  upon  rock.  (7)  The  rate  of  growth  of  the  different 
bodily  organs.  (8)  The  chemical  constitution  of  a  given  substance. 
(0)  The  significance  of  the  Biblical  version  of  Nebuchadnezar's  defeat. 
(10)  The  value  of  memory-training  In  Increasing  Intellectual  ability? 


CHAPTER  XXV 


DEDUCTION 


Nature  of  Deduction. — Deduction  is  the  reverse  of  induc- 
tion. Induction  reasons  from  speciflc  instances  to  a  iaw  or 
general  principle  exemplified  in  tliose  instances.  Deduction 
starts  from  a  law  or  general  principle,  and  reasons  from  the 
principle  to  its  consequences,  or  from  the  law  to  its  workings 
in  some  special  case.  Deduction  is  in  every  respect  fully  ai 
complex  as  induction,  and  may  malie  use  of  experimental 
abstraction  and  determination,  as  well  as  of  the  more  general 
and  simple  methods  of  analyais  and  syntheais.  Thus,  starting 
with  the  general  principle  that  life  In'-urance  is  a  good  thing 
and  that  we  ought  to  insure  our  lives  vith  the  t)est  possible 
company,  it  talces  a  great  deal  of  analysis  and  synthesis, 
abstraction  and  determination,  before  we  can  be  certain  which 
is  the  best  possible  company,  and  can  thus  apply  our  principle 
to  a  definite  instance.  Or  we  may  start  with  an  ethical  prin- 
ciple such  as  "All  rational  beings  as  such  are  to  be  treated  as 
ends-in-themselves,  and  not  as  mere  means  to  our  ends,"  and 
deduce  from  it  as  a  consequence  the  speciflc  principle  that 
children  and  imbeciles,  criminals  and  animals,  not  being  fully 
rational,  cannot  be  treated  in  this  way,  but  must  have  their 
"ends"  set  for  them  by  the  mor"  rational  elements  of  society. 
It  has  even  been  argued  by  men  of  hlph  education,  such  as 
Aristotle  and  even  Plato,  not  to  mention  more  modern 
instances,  such  as  Nietzsche,  that  people  of  relatively  low 
education,  and  all  animals,  are  definitely  to  be  exploited,  and 
find  their  highest  development  in  serving  the  higher  ends  of 
more  rational  people.  Just  how  far  this  principle  is  to  be 
applied  in  practise,  is  doubtful.  But  in  any  ease,  the  deduc- 
tion of  specific  consequence,  requires  special  experience,  and 
a  considerable  amount  of  abstraction  and  determination. 

One  of  the  aspects  of  deduction  which  makes  it  of  special 
value  as  a  method  of  scientific  investigation,  is  that  it  does 
not  require  a  law  to  be  already  established  in  order  to  have  a 
starting-point,  but  can  assume  a  hjrpothesis  provisionally,  and 

273 


274 


DEDUCTION 


t 
if 


then  ask.  Given  such  and  such  a  law,  what  would  follow  from 
It?  This  experimenting  with  mental  models  is  of  the  greatest 
value  when  we  are  dealing  with  complex  situations  into  which 
we  have  little  direct  insight.  For  example,  the  Copernican 
hypothesis  was  first  worked  out  in  this  provisional  and  experi- 
mental way,  until  the  coincidence  of  its  deduced  consequences 
with  the  observed  facts  made  it  universally  accepted.  So  also 
in  dealing  with  complex  geometrical  problems,  we  tend  to 
assume  various  hypotheses  and  ask  what  follows  from  them, 
until  w3  hit  upon  one  which  seems  acceptable.  The  same 
procedure  is  adopted  in  dealing  with  causal  models  also.  It  is 
even  possible,  in  cases  where  our  actual  knowledge  is  extremely 
slight,  for  us  to  assume  successively  (1)  a  certain  provi- 
sional hypothesis,  and  (2)  its  opposite,  and  then  deduce  con- 
sequences from  each  of  these  hypotheses  until,  by  means  of 
these  consequences,  we  succeed  in  bringing  our  assumptions 
into  contact  with  actual  or  possible  experience.  We  can  then 
decide  directly  between  fhe  groups  of  consequences,  and  thus 
indirectly  between  the  opposed  hypotheses.  This  we  do  fre- 
quently when  it  is  a  question  which  of  two  alternative  plans 
we  should  follow  in  some  complex  problem  of  conduct,  but 
the  "method  of  hypotheses,"  as  it  is  called,  has  been  employed 
in  philosophy  since  the  time  of  Zeno  and  Plato,  and  under  the 
name  of  "multiple  working  hypotheses"  is  employed,  in  a 
slightly  more  complex  form,  in  modern  science. 

Perhaps  the  most  noticeable  characteristic  of  deduction  is 
its  logical  consistency.  By  means  of  deduction  we  build  up 
mental  patterns  which  are  all  of  a  piece.  We  cannot  deny  a 
single  consequence  without  denying  the  principle  with  which 
we  started,  and  without  at  the  same  time  invalidating  all 
other  consequences  which  have  been  deduced  from  the  same 
principle.  If  we  can  deny  that  two  plus  two  make  four,  we 
are  at  the  same  time  denying,  not  only  the  truth  of  all  the 
principles  upon  which  arithmetic  rests,  but  also  the  whole 
body  of  the  science,  so  far  as  it  depends  upon  these  principles. 
We  are  denying,  for  instance,  that  2+4=6,  that  20 — 10=10, 
etc.  On  the  other  hand,  eacL  consequence  which  proves  accept- 
able, strengthens  the  main  principle,  and  also  an  argument  In 
favor  of  accepting  other  consequences.  If  this  medicine  was 
good  for  John,  when  he  had  the  measles,  and  for  M".ry  in 
similar  circumstances,  and  for  a  number  of  other  people  whom 
we  know,  then  It  will  be  good  for  us  too.    There  must  be  some 


AIM  OF  DEDUCTION 


275 


principle  underlying  the  previous  cases,  and  It  is  reasonable 
to  assume  that  our  case  also  will  come  under  that  principle. 
This  mode  of  thinking  is  especially  important  in  the  science 
of  healing,  but  applies  aiso  to  almost  all  of  the  more  developed 
sciences.  Where  observations  have  been  correlated  for  a  great 
number  of  years,  a  body  of  science  gradually  grows  up  which 
constitutes  a  system,  and  is  all  of  a  piece,  in  such  a  way  that 
we  can  confidently  apply  its  principles  even  beyond  the  hith- 
erto observed  types  of  case. 

As  a  method  of  scientific  investigation,  deduction  is  used 
chiefly  in  drawing  consequences  from  the  mental  models  which 
we  have  cbnstructed,  whether  these  models  are  merely  provi- 
sional, or  have  been  made  in  accordance  with  principles 
securely  established  upon  a  basis  of  constant  experience. 
These  consequences  may  then  be  compared  with  the  observed 
facts  or  with  the  known  laws  in  the  special  science  of  which 
they  form  a  part.  In  special  cases,  they  may  even  be  com- 
pared with  the  general  principles  of  consistency.  If  the  con- 
sequences do  not  agree  with  the  known  facts,  we  know  that 
the  model  we  have  assumed  for  the  purposes  of  understanding 
a  concrete  situation,  does  not  apply  to  that  situation.  If  they 
do  not  agree  with  what  are  regarded  as  known  laws  in  their 
special  field,  we  must  conclude  that  there  is  something  wrong, 
either  with  our  model,  or  with  the  "kno^n  laws" — if  not  with 
both.  If,  finally,  the  consequences  of  a  principle  lead  to  notice- 
able inconsistencies  among  themselves,  that  is  evidence  that 
the  model  itself  contains  logical  flaws,  and  has  been  wrongly 
constructed.!  The  nature  of  dei  tction,  then,  consists  In  rea- 
soning consistently  from  principles  to  consequences,  and  In 
scientific  investigation  more  particularly  consists  in  inferring 
to  the  consequences  involved  in  the  mental  models  which  we 
employ  for  our  various  scientific  purposes. 

Aim  of  Deduction  (A)  Objectivity.— The  consistency  which 
is  the  chief  characteristic  of  deduction  is  not  an  end  in  itself. 
For  purposes  of  scientific  investigation  our  aim  in  deducing 
consequences  is  to  get  into  touch  with  objective  facts  and 
laws.  Spinning  thought-webs  is,  in  itself,  valueless  to  the 
scientist.  He  is  interested  primarily  in  discovering  laws  and 
testing  the  objective  validity  of  hypotheses  in  his  special  field, 
and  thus  the  first  and  chief  aim  of  scientific  deduction  is 
objectivity.  Deduction  is  valuable  as  a  scientific  method  of 
investigation  precisely  so  far  as  it  brings  us  into  closer  touch 

iCf.  Plato,  Parmcnidet,  esp.  127E-128D. 


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DEDUCTION 


t  !l 


I 


with  the  objective  world  than  would  be  possible  without  Its 
aid.  Without  It,  we  might,  perhaps,  be  able  to  construct 
brilliant  hypotheses,  but  we  should  certainly  remain  unable 
to  verify  them  In  any  way,  or  even  to  choose  wisely  between 
rival  explanations  of  the  same  phenomenon,  because  we  should 
not  be  able  to  connect  them  up  with  our  empirical  observa- 
tions. A  great  portion  of  the  usefulness  of  deduction  to 
science,  consists  in  its  being  the  main  highway  along  which 
we  can  pass  from  our  mental  models  to  the  actual  facts,  and 
thus  verify  hypotheses  and  establish  laws.  Objectivity,  then, 
is  the  first  and  greatest  aim  of  deduction. 

(B)  Completeness. — In  the  second  place,  deduction  aims  at 
completeness,  or  at  least  at  reasonable  completeness,  a  com- 
pleteness such  as  sufficiently  ;ueets  our  problem  and  safe- 
guards our  conclusions.  We  do  not,  as  a  rule,  attempt  to 
deduce  all  the  possible  consequences  of  a  principle,  but  only 
the  more  striking  types  of  consequence,  and  more  especially 
such  consequences  as  can  be  brought  in  definite  relation  to 
the  concrete  situation,  and  can  furnish  "test  cases"  for  the 
mental  model  which  we  are  applying.  In  order,  however,  to 
realise  the  aim  of  objectivity,  it  is  necessary  for  us  to  avoid 
superficiality  and  one-sidedness,  and  thus  to  deduce  a  con- 
siderable variety  of  consequencef.  By  "reasonable  complete- 
ness," then,  is  understood  that  deduction  aims  at  drawing  a 
variety  of  consequences,  which  on  the  one  hand  are  appro- 
priate to  the  concrete  situation,  and  on  the  other  are  suflBcIent 
in  number  to  strengthen  our  conviction  of  the  objectivity  of 
our  procedure. 

How  Far  Realisable?  (A)  With  Mind-Made  Entities.— 
How  far  can  this  aim  be  realised?  How  far  Is  it  possible 
for  us  to  deduce  consequences  from  principles  In  a  way  which 
shall  be  both  objective  and  reasonably  complete?  Let  us  con- 
sider an  exampl".  If  we  understand  the  principle  which 
governs  the  working  of  our  psychological  puzzle-box,  we  can 
deduce  just  what  will  take  place  if,  e.  g.,  we  pull  the  two 
levers  In  the  wrong  order,  or  if  we  turn  the  box  on  its  white 
side  before  pulling  the  levers,  and  then  turn  It  back  agala 
before  pulling  the  second  lever;  or  If  we  turn  the  combina- 
tion lock  twice  to  the  right,  as  Indicated,  but  only  once  to 
the  left,  or  if  we  stop  at  the  wrong  figure,  eU:  So  too  If  we 
understand  the  principles  of  harmony  and  the  structure  of 
the  piano,  we  can  apply  our  knowledge  In  such  a  way  as 


AIM  OF  DEDUCTION 


277 


to  enumerate  the  chief  concords  and  discords,  and  explain  Just 
what  physical  phenomena— e.  g.,  in  the  way  of  "beats"— will 
take  place  when  such  and  such  notes  are  struck  together. 
In  such  capes  our  deductions  are  certainly  objective.  For  the 
object  to  which  we  refer  is  nothing  but  a  concrete  embodi- 
ment of  the  precise  principles  whose  implications  we  are 
making  explicit,  and  every  one  of  the  consequences  drawn 
can  be  verified  by  reference  to  the  facts.  In  dealing,  then,  with 
objects  of  this  kind,  where  the  object  is  constructed  In  terus 
of  a  plan  which  is  rational,  it  is  possible  to  deduce  the  con- 
sequences implied  in  the  principle  of  the  plan,  and  such 
consequences  will  be  found  to  hold  good  of  the  object  Itself. 

What  are  we  to  say  of  completeness?  If  such  deduction  is 
objectively  correct,  if,  e.  g.,  we  deduce  precisely  what  happens 
when  we  turn  the  combination  lock  only  once  to  the  left,  it 
could  not  well  be  more  complete — at  least  for  practical  pur- 
poses. It  is  true  that  a  physicist's  understanding  of  the 
nature  of  the  material  employed  and  the  various  physical 
laws  Involved  would  theoretically  be  more  complete,  though 
even  in  physics  any  final  completeness  is  out  of  the  question- 
But  the  problem  is  not  properly  concerned  with  .the  phyaical 
nature  of  the  material,  but  with  the  material  only  so  far  as 
it  is  the  embodiment  of  a  rational  plan.  Our  deduction  has 
solved  its  special  problem  completely.  But  if  we  regard  deduc- 
tion as  reasoning,  not  to  a  single  consequence  of  the  principle, 
but  rather  to  a  reasonably  complete  variety  of  consequences, 
so  that  the  truth  of  each  will  reflect  credence  upon  the  others 
and  will  also  strengthen  our  confidence  in  the  principle — we 
see  that  an  absolute  completeness  is  out  of  the  question.  The 
success  of  each  of  our  inferences  strengthens  the  conviction 
that  we  have  really  grasped  the  plan  according  to  which  the 
box  has  been  put  together,  and  our  aim  is  not  to  deduce  every 
last  consequence,  but  only  a  sufficient  variety  and  number  to 
avoid  one-sidedness  and  provide  an  adequate  test  of  the  prin- 
ciple. This,  however,  can  be  done,  In  the  case  of  the  box, 
and  in  the  case  of  the  piano,  and  it  seems  fair  to  state  that, 
sc  far  as  3ind-made  apparatus  is  concerned,  our  aim  can  be 
realised,  not  only  in  respect  of  objectivity,  but  also  in  respect 
of  completeness. 

Let  us  examine  another  example.  When  once  we  have 
grasped  the  principle  of  the  bi-litteral  cipher,  and  realise 
that  a  group  of  five  letters  is  to  represent  a  single  letter  of 


278 


DEDUCTION 


the  alphabet,  and  that  in  selecting  the  members  of  each  group 
we  are  restricted  to  some  combination  of  the  two  symbols 
A  and  B — we  can  deduce  at  least  as  many  consequences  as 
there  are  letters  of  the  alphabet.     Thus,  we  can  deduce  that 

AAAAB  =  a,   AAABA  =  h,  AABAA  =  c,  ABAAA  =  d 

etc.  In  fact,  the  reading  of  the  cipher  message  is  itself  a 
complex  consequence  of  the  principle,  and  the  most  convincing 
consequence  too.  The  drawing  of  consequences  is  in  such 
cases  a  kind  of  construction — for  by  this  means  we  construct 
the  details  of  the  mental  model  in  question — and  if  this  con- 
struction agrees  in  its  details  with  the  details  of  the  given 
problem  AAABB the  problem  is  solved.  Such  deduc- 
tion is  certainly  objective — for  it  enables  us  to  read  the 
cipher  message — and  reasonably  complete — for  it  enables  us 
to  construct  a  whole  alphabet,  and  indeed,  any  number  of 
cipher  messages  which  could  be  understood  by  the  transmitter 
of  the  original  problem.  If  such  examples  are  to  be  regarded 
as  typical,  we  may  state  that  in  dealing  with  mental  models, 
the  aim  of  deduction  can  be  realised. 

(B)  With  Natural  Phenomena. — We  deal  with  natural 
phenomena,  as  we  have  seen,  primarily  through  the  medium 
of  mental  models.  We  construct  a  model  in  terms  of  some 
rational  plan,  and  then  deduce  its  detailed  consequences  with 
a  view  to  comparing  these  with  the  details  of  the  phenomenon 
in  question.  If  the  mental  model  fits  the  phenomenon  in 
detail,  we  regard  the  principle  of  both  as  practically  identical,^ 
and  are  satisfied  that  we  have  practically  discovered  the  law 
of  the  phenomenon  in  question.  So  far  as  deduction  is  con- 
fined to  elaborating  the  consequences  of  our  mental  model, 
so  far  the  account  given  under  the  head  of  "mind-made 
entities"  holds  good.  But  in  dealing  with  natural  phenomena, 
we  mean  something  more.  Does  our  deduction  in  any  sense 
take  us  beyond  the  realm  of  mind-made  models,  and  bring 
us  into  contact  with  the  objective  world?  Is  deduction  objec- 
tive In  this  sense?  Let  us  consider  an  example.  In  trying 
to  understand  the  principle  of  the  basilar  membrane,  some 
scientists  use  the  model  of  the  wires  in  a  grand  piano,  while 
another  group  use  the  model  of  the  membrane  in  a  telephone. 
In  both  cases,  consequences  are  deduced  from  the  nature  of 
these  models  and  compared  with  the  experimental  evidence. 


1  Cf.  William  James,  Pragmatism,  lecture  I. 


TYPES  OF  DEDUCTION 


279 


Has  this  kind  of  deduction  a  significance  which  is  objective? 
Yes.  it  certainly  does  help  to  bring  us  into  closer  and  more 
intimate  contact  with  the  meaning  of  the  phenomena  in 
question.  It  is  not  at  the  present  day  pos^ble  to  state  that 
either  of  these  models  is  perfectly  correct,  but  the  deduction 
of  consequences  from  both  models,  and  the  experimental 
attempts  to  verify  the  theoratical  deductions  in  terms  of 
the  actual  fact-^  have  undoubtedly  led  to  a  great  increase 
in  our  knowledge  of  the  objective  conditions  and  facts  of  the 
case.  So  far,  t;  on,  as  objectivity  is  concerned,  the  aim  of 
deduction  can  be  at  least  partially  realised  in  this  field. 

In  respect  of  completeness  also  something  can  be  done.  The 
deductions  as  such  are  from  the  principle  of  the  mental  model 
to  the  details  of  the  mental  model,  and  so  far  as  our  thought 
is  confined  to  the  realm  of  mental  models,  each  such  deduc- 
tion can  be  regarded  as  complete.  But  when  y>e  transfer  the 
question  to  the  world  of  natural  objects,  this  is  no  longer  the 
case.  There  is,  as  we  have  already  seen,  always  a  certain 
gap  which  separates  our  models  from  the  concrete  realities. 
The  reality  is  always  something  more  detailed,  for  instance, 
than  we  seem  quite  able  to  grasp.  Nature,  as  we  say,  has  an 
Infinite  variety.  This  gap,  this  difference  between  what  we 
seem  able  to  construct  on  the  one  hand,  and  the  objective 
phenomena  on  the  other,  is  a  measure  of  the  extent  by  which 
we  fall  short  of  completeness.  We  cannot  deduce  all  the 
details  of  the  phenomenon  because  we  have  not  perfect  insight 
into  the  law  in  question.  Certain  of  the  more  important  and 
striking  consequences  we  can  deduce,  where  our  knowledge 
is  well  developed.  But  completeness  is  more  than  we  can 
expect.  In  dealing,  then,  with  natural  phenomena,  the  aim 
of  deduction,  in  point  of  objectivity  and  completeness,  can 
only  partially  be  realised.  This  partial  realisation,  however, 
is  certainly  valuable,  not  only  in  itself,  but  also  as  leading 
to  further  progress  in  scientific  discovery. 

Types  of  Deduction. — There  are  two  main  types  of  deduc- 
tion, the  mathematical  and  the  causal.  That  is  to  say,  we 
can  distinguish  deductions  in  terms  of  the  type  of  mental 
model  whose  consequences  are  deduced,  and — as  we  have 
already  seen — the  most  commonly  found,  and  most  generally 
valuable  types  of  mental  models  are  precisely  those  which 
belong  to  the  mathematical  and  causal  groups.  But  mental 
models  are  by  no  means  confined  to  these  two  types.    On 


280 


DKUUCTION 


the  contrary,  there  are  at  least  as  many  possible  types  as 
there  are  specifically  distinct  scientific  viewpoints.  But  these 
are  indefinite  in  number,  and  are  also  tending  to  Increase  as 
science  takes  in  more  fields  of  Inquiry,  and  it  is  thus  not,  per- 
haps, possible  to  confine  within  any  rigid  limits  the  number 
and  types  of  mental  models.  In  consequence,  we  cannot 
restrict  in  any  way  the  number  of  typical  forms  which  can 
be  used  in  valid  deduction.  The  types  of  deduction  are  innu- 
merable. In  the  history  of  logic,  attempts  have,  indeed,  been 
made  to  work  out  all  the  forms  of  valid  deduction  which  the 
mind  could  possibly  use,  but  as  the  most  notable  attempt 
restricted  thought  to  following  the  detailed  developments  of 
a  single  mental  model,  and  that  too  neither  quantitative  nor 
causal2 — we  must  regard  it  as  bold  but  unprofitable.  Thought 
cannot  be  restricted  to  the  use  of  any  single  group  of  models, 
but  is  as  various  and  complex  as  it  finds  advisable  in  dealing 
with  the  problems  which  arise.  As  it  is  clearly  impossible  to 
limit  such  problems,  so  it  is  impossible  to  limit  the  forms  of 
deduction  which  can  be  used  in  solving  those  problems. 
Thought  is  free  and  unfettered.  All  we  can  safely  say  is 
that,  at  the  present  stage  of  science,  the  mathematical  and 
causal  types  are  the  most  frequent  and  the  most  universally 
valuable. 

Validity  of  Deduction. — That  deduction  is  not  always  objec- 
tively valid  will  be  plain  if  we  consider  briefly  a  few  typical 
cases.  Hemlock  Jones  in  the  story  deduces  with  convincing 
clearness  that  Potson  has  stolen  his  pipe — and  the  pipe  is,  in 
fact,  in  Potson's  pocket.  Potson  realises  that  it  would  be 
quite  impossible  to  convince  Jones  that  his  ingenious  deduc- 
tion is  invalid,  though  he  knows  it  to  be  wrong.  So  too  the 
paranoiac  deduces  with  almost  flawless  completeness  that  all 
the  world  is  in  a  conspiracy  against  him — and  indeed  they  do 
actually  put  him  una  r  restraint  in  the  end.  It  would  be  quite 
impossible  to  persuade  him  that  his  deductions  are  unsound, 
and  yet  we  know  that  they  are.  It  is  possible,  in  short,  to 
explain  one  and  the  same  fact  in  terms  of  a  variety  of  mental 
models,  and  yet  certain  of  those  mental  models  may  be  radi- 
cally mistaken,  as  when  Bain  tries  to  explain  parental  affec- 
tion in  terms  of  the  benefits  to  be  returned  in  after-years,  or 

2  The  reference  Is  to  the  Aristotelian  syVogiam.  Aristotle  himself 
believed  this  to  be  a  cautal  model,  the  "middle  term"  being  Identical 
with  the  canKP.     Bnt  this  Is  today  generally  regarded  as  a  mistake. 


I  ) 


VALIDITY  OF  DEDUCTION 


281 


Mill  tries  to  explain  universal  benevolence  in  terms  of  ego- 
istic self-seeking.  There  are  thus  cases  of  deduction  which 
seem  convincing  enough  from  the  viewpoint  of  consistency 
alone,  but  are  found  to  be  inadequate  when  we  apply  them 
to  the  actual  world.  What,  then,  is  the  criterion?  How  are 
we  to  distinguish  a  valid  from  an  invalid  deduction?  To  this 
question  we  can  only  answer  that  there  is  no  simple  criterion. 
In  order  to  test  our  deductions  and  discover  whether  they  are 
objectively  valid  or  not,  our  only  final  criterion  is  the  progress 
of  science  Itself.  If  the  mental  model  which  we  have  used  is 
found  to  be  helpful  in  the  concrete  situation,  and  also  fruitful 
in  suggesting  and  solving  further  problems — if,  in  short,  it 
"works" — we  may  regard  it  as  so  far  valid.  If,  however,  like 
Bain's  insurance  model  applied  to  the  case  of  family  affec- 
tion. It  seems  to  solve  the  case  before  us,  but  brings  us  into 
hopeless  conflict  with  the  models  of  explanation  accepted  as 
verified  in  all  kindred  researches,  uid  is  of  no  avail  to  solve 
further  problems — there  is  so  far  reason  to  regard  it  as  invalid. 
In  the  case  of  natural  science,  then,  the  only  adequate  test 
of  the  objective  validity  of  deduction  is  the  further  progress 
of  the  science  itself.  In  the  case  of  mind-made  entities,  how- 
ever, we  have  already  seen  that  deduction  can  be  objective. 
In  such  cases  it  is  a  mere  matter  of  consistency,  and  of  that 
we  are  fairly  good  judges,  especially  in  the  simpler  instances. 
In  complex  cases,  analysis  is  necessary,  and  only  the 
advanced  thinker  can  come  to  valid  decisions. 

Summary. — Deduction,  then,  is  a  process  which  makes 
explicit  the  consequences  implied  by  some  principle  or  law, 
whether  such  law  is  already  established,  or  is  merely  assumed 
as  a  provisional  hypothesis.  Its  chief  aim  is  to  bring  us  Into 
closer  touch  with  the  objective  facts  than  would  be  possible 
without  its  aid,  and  to  be  not  only  objective,  but  also  reason- 
ably complete.  This  aim  we  can  accomplish  in  dealing  with 
mental  models,  but  can  only  approximate  to  attaining  In  the 
case  of  natural  phenomena.  In  such  cases  the  validity  of  our 
deductions  can  be  appreciated  only  as  science  itself  advances 
by  such  means.  In  general,  however,  it  may  be  confidently 
asserted  that  deduction  t«  a  valuable  factor  in  securing  such 
an  advance. 

FOR  FURTHER  READING 

Chr.  Sigwart.  Logic,  Vol.  II,  pp.  181-192.     W.  Wundt,  Logik,  (3rd 
Edit.),  Vol.  II,  pp.  30-38. 


s ; 


..■'? 


282 


DEDUCTION 


,li 


£XKUCI8l!» 

How  might  tlie  following  case*  be  Investigated  deductively:  (1) 
The  comparative  efficiency  of  learning  a  long  poem  as  a  whole,  or 
ma  a  number  of  Rectlona.  (2)  The  value  of  the  ergograph  as  a  tent 
of  mental  fatigue.  (3)  Whether  black  fs  or  Is  not  a  positive  aensa- 
tlon.  (4)  The  best  method  of  holding  the  hand  In  writing.  (5)  The 
moat  efficient  method  of  practising  at  the  piano  or  violin.  (6)  The 
scientific  value  of  psychological  or  pedagogical  study.  (7)  The  best 
time  for  planting  corn.  (8)  The  means  by  which  the  automatic  chess- 
player (described  by  E.  A.  Poe)  was  worked.  (»)  The  practical 
value  of  a  college  education.  (10)  One  of  the  Sherlock  Holmes 
problem!  V 


hs 


hi 

M 


CHAPTER  XXVI 
INDUCTION  AND  DEDUCTION 

The  Problem.— Owing  to  historical  associations,  induction 
and  deduction  have  become  watchwords  of  scientlflc  and 
logical  thought.  Many  of  our  elementary  manuals  to  this  day 
are  entitled  "Logic,  Deductive  and  Inductive,"  as  though 
deduction  ard  induction  together  exhausted  the  field  of  logical 
inquiry.  There  are  even  well-known  books  published  on 
Deductive  Logic  alone,  and  on  Inductive  Logic  alone,  and 
many  writers  who  treat  of  both,  do  so  in  separate  volumes. 
We  have,  then,  a  tendency,  owing  to  historical  considera- 
tions.! to  regard  induction  and  deduction  as  separate,  and 
even  opposed,  methods.  Deduction,  in  our  minds,  stands  for 
Aristotle  and  mediaeval  thought  with  its  emphasis  on  argu- 
mentation and  clear  ideas,  and  its  almost  total  lack  of  experi- 
mentation and  discovery.  Induction  similarly  stands  for  mod- 
em science,  with  all  its  empiricism  and  distaste  for  arm-chair 
methods,  and  with  its  extreme  insistence  upon  observation 
and  experiment.  We  even  tend  to  think  of  deduction  as  the 
method  of  mere  proof,  of  organisation  of  knowledge  obtained 
from  some  non-deductive  source,  while  induction  seems  to  us 
to  be  the  method  par  excellence  of  scientiflc  investigation, 
the  method  of  discovery,  the  genuine  source  from  which  all 
knowledge  comes.  For  the  popular  consciousness,  then,  the 
two  methods  are  sharply  distinct  and  even  opposed. 

Fbr  the  scientific  consciousness,  on  the  other  hand,  they  are 
at  the  present  day  recognised  as  working  hand  in  hand,  and 
indeed  as  a  method  of  investigation  deduction  tends  to  be 
preferred,  at  least  in  the  more  advanced  and  exact  sciences.2 
The  popular  view  rests  upon  the  idea  that  for  deduction,  the 
law  which  forms  its  starting-point  must  have  been  already 
established,  whereas  for  the  scientist  the  most  fruitful  char- 
acteristic of  deduction  consists  precisely  in  the  fact  that  Its 


1  Cf.  Goblot,  Traite  de  Logique,  pp.  82-83. 
2Cf.  Wundt,  Logik,  3e  AuflajfP,  Vol.  IT.  p.  31. 

283 


284 


INDUCTION  AND  DI'.DUCTION 


Btarting-point  may  equally  well  be  a  provisional  hypotheHls, 
asBumed  deliberately  for  purposeH  of  experimentation.  For 
the  Bclentiflc  consciousness,  then,  the  old  and  sharp  distinc- 
tion of  function  which  the  popular  consciousness  still  retains, 
has  broken  down,  and  it  is  conceivable,  since  both  methods 
are  found  to  worlc  together  in  science,  that  they  may  not  be 
so  sharply  distinct  as  is  usually  supposed. 

The  problem  of  the  present  chapter  is  to  examine  the  rela- 
tion of  induction  and  deduction  to  one  another.  In  order  to 
discover  whether  they  are  two  distinct  methods,  as  the  popu- 
lar consciousness  and  even  many  scientists  still  suppose,  or 
whether  they  are  two  correlative  aspects  of  a  single  method 
of  scientific  investigation,  as  perhaps  a  majority  of  scientists 
and  logicians  at  the  present  day  tend  to  believe.  We  shall 
begin  by  inquiring  whether  induction  necessarily  involves 
deductive  elements,  and  shall  then  pass  on  to  the  question 
as  to  whether  deduction  necessarily  involves  inductive  ele- 
ments as  an  integral  portion  of  its  method  In  investigation. 

Does  Induction  Involve  Deduction? — Let  us  examine  a  typ- 
ical case  of  induction.  We  recognised  provisionally  two  main 
types  of  induction,  in  the  former  of  which  abstraction  seemed 
more  prominent,  while  in  the  latter  greater  emphasis  seemed 
to  be  laid  upon  determination.  Subsequently,  we  threw  doubt 
upon  any  attempt  to  draw  a  hard  and  fast  distinction  between 
these  two  types,  but  for  the  sake  of  completeness  we  shall 
here  examine  cases  from  each  group.  Let  us  consider  first 
a  case  which  belongs  more  to  the  abstraction-type.  The  prob- 
lem beir.^  to  discover  whether  there  Is,  in  point  of  fact,  a 
law  of  "general  intelligence"  pervading  our  activities  in  dif- 
ferent fields  of  work,  we  proceed  by  selecting  a  great  variety 
of  experimental  tests,  designed  to  probe  our  processes  of 
attention,  memory,  reasoning,  etc.,  and  giving  these  to  a  group 
of  subjects  whose  ranking,  in  respect  of  Intelligence,  Is 
already  ascertained,  at  least  in  part,  by  other  means.  Let 
us  assume  that  the  ascertained  order  of  the  fubjects  Is  A,  B, 
C,  D,  .  .  .  ,  and  that  the  results  of  our  experiments  are 
as  follows: 


11: 
|i  ) 


No.  of  Test. 

1 

2 

.*»       } 

5 

6 

7 

8 

9 

io 

Order  of  Subject  A 

2 

1 

1       1 

1 

1 

1 

2 

1 

1 

B 

4 

3 

6       3 

2 

2 

2 

1 

3 

2 

C 

7 

5 

3"  9 

3 

3 

5 

3 

2 

3 

D 

6 

4 

4       8 

8 

7 

6 

6 

7 

4 

INDUCTION  AND  DEDUCTION 


These  flfurea  represent  the  work  of  the  preliminary  anal- 
ysis and  synthesis.  We  proceed  to  abstract  and  determine 
the  final  ranking  of  the  subjects  by  abstractinf  the  average  of 
the  various  test-results  for  each  subject,  and  then  arranging 
the  subject  accordingly.  In  the  end,  we  find  that  our  con* 
elusions  agree  with  the  previously  ascertained  order.  Our 
tests  also  rank  the  subjects  in  the  order  A,  B.  C,  D.  .  .  . 
That  is  to  say,  the  subject  who  is  considered  most  intelligent 
by  other  standards  really  leads  in  most  of  the  tests,  and  the 
subject  who  is  considered  poorest  really  is  last  In  most  of 
the  tests,  etc.  So  far,  then,  as  these  particular  tests  go,  it 
looks  as  though  there  might  conceivably  be  some  such  entity 
as  "general  Intelligence"  manifesting  itself  in  solving  prob- 
lems of  any  and  every  kind. 

Does  deduction  play  any  part  in  the  above  inquiry?  Yes, 
it  certainly  does.  We  deduce  that  general  Intelligence — 
assuming  that  there  is  such  a  thing— must  be  such  as  to  make 
its  possessor  do  well  in  any  kind  of  test.  That  is  to  say.  we 
deduce  the  specific  consequences,  that  A — supposed  to  be  the 
most  intelligent  subject — will  come  out  first  In  test  1.  In 
test  2,  in  test  3  .  .  .  ,  that  the  least  intelligent  subject 
will  come  out  last  in  test  1.  in  test  2  .  .  .  etc.  It  is 
because  our  experimental  results  on  the  whole  bear  out  these 
deductions,  that  we  consider  it  reasonable,  so  far  as  this  evi- 
dence goes,  to  suppose  that  there  may  be  such  a  thing  as 
general  intelligence.  That  is  to  say,  without  some  such  deduc- 
tions, we  should  not  be  able  to  establish  or  even  to  reject  the 
suggestion.  For  even  if  the  results  had  not  borne  out  our 
deductions,  but  had  led  to  negative  conclusions,  the  deduc- 
tion would  still  have  played  an  essential  part.  It  Is,  in  fact, 
only  by  reference  to  consequences  deduced  from  an  assumed 
principJe,  that  we  can  be  sure  that  the  facts  establish  a  law, 
or  reject  it,  or  leave  it  not  proven.  Deduction,  then,  is  an 
essential  and  integral  part  of  the  inductive  method  by  means 
of  which  we  establish  laws. 

Let  us  take  another  example,  In  which  the  determination- 
aspect  Is  more  prominent  than  the  abstraction-aspect.  Is 
playing  the  piano,  or  in  writing  with  a  type-writer,  we  are 
able  to  estimate  certain  spatial  relations  with  great  accuracy, 
as  is  shown  by  the  way  in  which  *e  can  strike  almost  any 
key  we  wish,  without  looking  at  it.  What  is  the  principle  or 
law  underlying  this  accuracy?    We  can  investigate  the  ques- 


286 


INDUCTION  AND  DKDUCTION 


tion  by  flrst  constructing  a  mental  model  In  Its  general  out 
linen,  and  then  working  out  Its  detallH  and  seeing  how  these 
compare  with  the  experlnientnl  reHultH.  Accuracy  in  motor 
localisation  muHt  depend  upon  Honiething  In  our  HenHe-organs. 
We  muHt  have  xonie  Hensory  organ  capable  of  eHtlmating  Hpatial 
movements  with  accuracy.  In  the  case  of  the  arm,  there  are 
only  three  po8HibU>  factorH — (1)  the  nkin,  (2)  he  muscles  and 
tendons,  and  CI)  the  Jolntu  at  wrint,  elbow,  and  shoulder.  We 
assume  that  if  one  of  theue  plays  a  great  jmrt  in  such  local- 
isation, treating  it  in  such  a  way  as  to  paralyse  it  for  the  time 
being  will  interfere  with  our  accuracy,  and  conversely,  if 
throwing  one  of  these  factors  out  of  gear  makes  no  appre- 
ciable difference  to  our  accuracy,  It  is  not  seriously  con- 
cerned in  our  estimation  of  movement.  Thus  if  the  skin  is 
sprayed  with  ethyl  chloride,  it  becomes  frozen,  and  its  sen- 
sitivity is  much  impaired.  If  tMe  skin  is  a  vital  element  in 
estimating  movements,  we  should  expect  our  accuracy  to 
diminish,  and  conversely,  if  our  accuracy  does  not  diminish, 
we  should  regard  the  skin  a.s  not  playing  an  important  part 
in  such  localisation.  That  whose  presence  or  absence  makes 
no  apparent  difference  to  the  phenomenon,  cannot  be  causally 
connected  with  the  phenomenon.  Similarly  with  the  muscles 
and  the  joints.  Experiments  are  devised  which  impair  the 
sensitivity  of  one  of  these  factors  for  the  time  being,  and 
our  accuracy  is  te.sted  in  the  same  way  as  with  the  skin. 
It  was  discovered  by  experiments  of  this  type  that  the  mus- 
cles play  a  certain  part,  but  not  a  very  great  one,  and  that 
the  chief  part  is  probably  played  by  the  joints."!  That  is  to 
say,  the  experiments  bore  out  certain  of  our  expectations,  and 
refuted  others. 

In  such  cases  there  Is  no  necessity  for  minute  inquiry.  We 
very  obviously  deduce  the  consequences  of  our  assumed 
hypothesis,  and  this  is,  In  fact,  often  referred  to  as  a  portion 
of  the  "deductive  method  of  Induction."  So  far,  then,  as 
the  determination-type  of  induction  is  concerned,  we  may 
regard  it  as  admitted  that  it  is  furdamentally  deductive. 
We  may  also  note  that  a  precisely  similar  deduction  of  the 
consequences  of  a  mental  model  plays  a  part  also  in  the 
abstraction-type.     We  there  deduced  what  consequences  should 


3<'f.  «iol(l8chelder'»  n.aper  In  Arcliir.  fiir  Anatnmir  unil  PhfiHinlogiv, 
1889.  pp.  :{«!>,  .">4<»  Also  .lames.  I'lhicipha  of  I'sjjcliolufiu,  Vol.  11. 
pp.   189  ff. 


INDUCTION  AND  DEDUCTION 


287 


hold  food  if  the  theory  of  general  Intelligence  was  to  be 
upheld.  That  lo  to  say,  we  made  explicit  which  wa '  logically 
Involved  In  such  a  theory — vix.  that  A  would  be  drat  In  testa 
MO,  etc.  If  such  cases  may  be  regarded  us  typlcsl,  our  con> 
elusion  Is,  that  induction  as  such  necessarily  Involves  the  uie 
of  deduction,  as  an  esnential  part  of  the  method  of  discover- 
ing laws. 

Does  Deduction  involve  Induction?— Ooldachelder's  experi- 
ment with  the  skin,  miiHcleR,  and  joints  illustrates  the  deduc- 
tive method  of  induction,  and  in  dealing  with  that  aspect  of 
deduction  which  is  found  useful  as  a  method  of  investtKation, 
It  would  be  ditncult  to  And  a  more  typical  case  of  deduc- 
tion. The  use  of  deduction,  in  actual  practise,  is  to  construct 
In  its  details  a  mental  model  already  constructed  In  general 
outline — to  deduce  the  detrtlled  consequences  which  follow 
from  the  original  plan— In  order  to  see  how  these  compare 
with  the  experimental  or  observed  results.  If  the  two  coin- 
cide in  detail,  the  principle  exemplified  in  the  mental  model 
is  regarded  as  so  far  eHtabl.  -  :d.  In  Euclid's  well-knowr 
proof  of  Bk.  I,  prop  4,  th'  method  of  superposition  is 
employed.  The  deductive  element  in  th's  method  consists  in 
the  argument  that  if  the  triangle  ABC  is  superimposed  upon 
the  triangle  DEF,  so  that  the  side  AB  falls  upon  the  side  DE, 
and  the  side  AC  upon  the  side  DF,  the  plan  of  structure  is 
such  that  B  must  coincide  with  E,  and  C  with  F,  and  the  base 
BC  must — as  a  further  deduced  consequence — coincide  with 
the  base  EF,  so  that  the  triangles  will  be  found  to  be  equal 
in  all  respects.  The  establishment  of  the  principle  consists 
In  experimenting  by  means  of  superpoBition,  and  finding  that 
the  experimental  result  does  actually  bear  out  the  conse- 
quences, in  proportion  as  It  is  carried  out  correctly, — and 
indeed  cannot  do  otherwise.  So  too  In  the  cause-effect  model, 
wc  reason  that  when,  if  A  is  present  X  is  always  present,  and 
If  A  Is  absent  X  Is  always  absent,  and  if  X  is  present  A  Is 
always  present,  and  if  X  Is  absent  A  is  always  absent, — then 
A  and  X  are  causally  connected.  These  specific  deductions 
represent  in  fact  the  detailed  nature  of  the  cause-effect 
mental  model.  Whether  causal  connection  is  or  is  not  estab- 
lished in  a  particular  case,  depends  on  whether  the  experi- 
mental or  observed  results  coincide  with  the  details  of  this 
model,  or  fail  to  coincide,  respectively. 

In  scientific  investigation,  then,  inductioi.  always  contains 


288 


INDUCTION  AND  DEDUCTION 


i 


deduction  of  consequences  as  a  part  of  the  Inductive  discovery 
of  laws.  But  does  deduction  always  necessarily  contain 
induction?  Can  we  perhaps  maintain  that  induction  con- 
nects up  a  mental  model  with  the  facts,  and  thus  comes  into 
play  only  when  we  go  beyond  the  mental  model  and  try  to 
bring  it  into  contact  with  something  which  is  not  a  mental 
model — the  actual  objective  phenomena?  If  so,  it  looks  as 
though  when  thought  was  merely  concerned  with  itself,  we 
might  have  a  deduction  of  consequences  without  the  slightest 
reference  to  the  world  of  natural  phenomena — i.  e.,  a  case  of 
pure  deduction,  unmixed  with  anything  empirical  and  induc- 
tive. It  is  sometimes  thought  that  Euclid's  reasonings  are  of 
this  kind.     Can  we  do  tnis,  or  is  It  impossible? 

Let  us  consider  the  actual  facts.  In  the  first  place,  if  this 
were  possible,  should  we  not  have  a  case  of  "pure"  thought — 
of  thought  thinking  itself  without  reference  to  the  sense- 
perceivable  world?  nut  this  is  the  kind  of  thought  sometimes 
attributed  to  infinite  Beings — i.  e.,  is  a  transcendent  mode  of 
thought  which  human  beings  do  not  seem  to  possess.  In  the 
second  place,  we  find  that  it  is  at  least  possible  to  use  induc- 
tion in  dealing  with  mental  models — as  when  we  are  seeking 
to  discover  the  key  to  a  cipher,  or  to  make  our  way  into  the 
puzzle  box,  or  to  solve  a  geometrical  or  algebraical  problem. 
And  in  the  third  place,  if  we  examine  the  mathematical  and 
cau<;al  models  exemplified  above,  we  find  that  there  is  an 
Inductive  element  which  appears  essential  to  the  deduction 
Itself,  so  far  at  least  as  that  deduction  constitutes  a  method 
cf  investigation.  In  the  case  from  Euclid,  the  inductive  por- 
tion of  the  method  consists  in  the  experiment  of  superposition 
Itself,  and  in  seeing  that  when  the  triargle  ABC  is  superim- 
posed upon  the  triangle  DEF,  they  do  In  fact  coincide.  Inci- 
dentally, in  the  deduction  of  each  individual  consequence 
there  is  involved  a  reference  to  the  actual  construction  of  the 
figure,  and  the  verification  of  this  reference  is  certainly  induc- 
tive In  nature.  When  we  apply  the  side  AB  to  the  side  DE 
so  that  the  point  A  falls  upon  the  point  D,  induction  is 
needed  to  verify  the  deduced  consequence  that  the  point  B 
coincides  with  the  point  E,  and  so  also  with  the  other  deduc- 
tions. To  each  deduction  of  consequences  there  is  a  corre- 
sponding induction,  and  in  fact  we  always  proceed  in  this 
double  way,  comparing  the  mental  plan  with  the  actual 
details,  and  the  actual  details  with  the  mental  plan.    So  too 


INDUCTION  AND  DEDUCTION 


289 


in  appl3ing  the  causal  model,  both  in  respect  of  its  nature  as 
a  model,  and  in  respect  of  its  application  to  the  world  of 
events  and  processes  in  time.  So  far  as  the  model  itself  is 
concerned,  each  deduced  consequence  <s  accompanied  by  an 
inducti  m  \rhich  verifies  it,  and  so  far  as  ♦he  application  to 
the  empirical  world  is  concerned,  so  well  is  it  known  that  for 
each  deduction  there  is  a  corresponding  indiction,  that  the 
causal  model  is  frequently  taker  as  the  typic;il  model  which 
represent  inductive  procedure,  and  in  fact  Is  often  regarded 
as  though  it  belonged  exclusively  to  induction  If  these  exam- 
ples may  be  regarded  as  typical,  then  we  can  state  that  every 
deduction,  as  such,  is  necessarily  accompanied  by  a  corre- 
sponding induction  which  verifies  and  confirms  it — that  is  to 
say,  deduction  necessarily  Involves  induction. 

The  Inductive-Deductive  Method. — Induction  and  deduction, 
then,  necessarily  involve  one  another,  and  thus  turn  out  to  be 
two  aspects  of  a  single  fundamental  method  of  investigation. 
In  the  first  place,  they  are  two  aspects,  correlative  but  dls- 
■  tlnct.  In  respect  of  starting-point,  conclusion,  and  method, 
one  special  aspect  stands  out  more  prominently  in  the  case 
which  we  call  induction,  and  the  other  aspect  is  more  promi- 
nent in  the  case  which  we  call  deduction.  In  induction  we 
appear  lo  be  starting  from  an  analysed  and  determined  situ- 
ation, and  to  conclude  to  a  law.  In  deduction  we  appear  to 
^tart  with  a  law,  and  to  conclude  with  a  group  of  conse- 
quences which  together  constitute  an  analysed  and  deter- 
mined situation.  But  these  differences  are  only  apparent. 
The  appearance  arises  from  one-sided  emphasis,  and  if  we 
look  a  little  more  closely  into  induction  we  see  that  it  starts 
just  as  much  with  a  mental  model,  provisionally  assumed  as 
incorporating  the  law  which  it  is  sought  to  establish,  as  with 
the  situation  to  which  such  a  model  is  assumed  to  apply.  So 
too  it  concludes  just  as  much  with  the  application,  to  its  data, 
of  a  set  of  consequences  deduced  from  the  mental  model,  as 
with  insight  into  a  law.  In  fact,  application  of  deduced  con- 
sequences to  the  data  is  the  way  in  which  we  obtain  insight 
into  the  law.  So  also  in  the  case  of  deduction  in  its  use  as  a 
method  of  investigation,  if  we  look  a  little  more  closely,  we 
see  that  its  starting-point  is  not  just  some  mental  model  in 
general,  but  a  specific  mental  model  which  is  adapted  to  the 
(lata.  That  is  to  say.  we  start  just  as  much  with  the  data  of 
the  problem  as  with  the  law  or  mental  model,  and  we  conclude 


I 


i. 


290 


INDUCTION  AND  DEDUCTION 


just  as  much  with  establishing  the  law  as  with  deducin ,  con- 
sequences. And  in  respect  of  method,  we  see  that  (1)  viewed 
asinference  from  law  to  consequences  it  may  be  calkd  deduc- 
tive, but  viewed  as  verifiable  consequences,  as  consequences 
legitimately  inferred  from  the  model  in  question  definitely 
applying  to  the  data,  there  is  an  inductive  reference  to  the 
detailed  features  of  the  situation.  In  othar  words,  the  method 
has  both  an  Inductive  and  a  deductive  aspect,  and  these  are 
thus  two  correlative  and  interdependent  aspects  of  a  method 
which  is,  however,  fundamentally  one. 

The  function  of  the  inductive-deductive  method  is,  to  sum 
up  and  carry  through  the  work  begun  by  analysis  and  synthe- 
sis, abstraction  and  determination.  In  fact  these  three 
methods,  (1)  analysis-synthesis,  (2)  abstraction-determina- 
tion, and  <^)  induction-deduction,  may  be  regarded  as  three 
successive  stages  or  phases  of  one  and  the  same  general 
method— the  method  of  scientific  investigation.  In  the  first 
place,  they  are  successive.  Analysis  and  synthesis  are  pre- 
liminary methods,  and  are  content  with  being  able  to  take 
apart  and  put  together  again  the  problem  under  investigation, 
which  is  usually  a  concrete  situation.  Abstraction  and  deter- 
mination are  more  advanced  methods,  and,  starting  with  a 
situation  already  analysed  and  synthesised,  single  out  some 
element  or  aspect  for  special  consideration,  and  by  thus  con- 
centrating their  activities  in  a  single  direction,  are  enabled 
to  go  further  than  was  possible  for  analysis  and  synthesis. 
At  the  same  time,  they  do  not  go  so  far  as  Induction  and 
deduction,  but  are  satisfied  if  they  take  a  single  element  out 
of  one  context  and  determine  it  by  reference  +0  another  con- 
text. Induction  and  deduction  are  highly  complex  methods 
which  make  use  of  both  the  foregoing  methodr,  and  carry  their 
work  further  until  we  succeed  in  discovering  some  law  and 
its  application  to  a  situation  which  has  been  analysed  and 
determined. 

In  the  second  place,  these  methods  are  not  merely  succes- 
sive, but  are  also  phases  of  one  and  the  same  fundamental 
method,  the  method  of  scientific  investigation.  This  we  can 
realise  from  the  following  considerations:— (1)  Analysis  and 
synthesis  involve,  as  we  saw,  insight  into  the  law  of  the  phe- 
nomenon to  be  analysed  and  synthesised.  So  too  with 
abstraction  and  determination,  while  induction  and  deduction 
are  concerned  with  insight  into  the  same  law.    (2)  The  aim 


SCIENTIFIC  INVESTIGATION 


291 


of  all  three  methods  la  one  and  the  same — viz.  objectivity 
and  completeness.  They  are  concerned  with  the  same  objects, 
for  all  alike  are  trying  to  bring  us  into  contact  with  the  world 
in  which  we  actually  live.  (3)  Finally,  the  method  is  funda- 
mentally the  same.  In  all  three  cases  we  proceed  by  the  con- 
struction of  mental  models  and  their  application  to  the  facts 
of  the  situation. 

Summary — Scientific  investigation. — There  is  thus  one  fun- 
damental method  of  scientific  investigation,  in  which  we  have 
distinguished  three  phases,  (1)  the  pnaly tic-synthetic,  (2)  the 
abstractive-determinative,  and  (3)  the  inductive-deductive. 
The  function  of  this  method  is  to  enable  us  to  understand  the 
world  in  which  we  live,  and  to  understand  it  objectively — 
i.  e.,  in  its  own  nature — and  as  completely  as  is  possible  for 
us.  This  fu  iction  is  accomplished  by  the  construction  of 
mental  mod  s  which  we  can  fully  understand,  and  their  appli- 
cation to  the  special  problems  and  situations  which  arise  for 
us.  A  perfect  application  of  our  mental  models  to  natural 
phenomena  is  not  quite  possible.  There  is  always  a  certain 
incompleteness,  a  gap  of  some  sort  between  the  rational 
model  and  the  actual  concrete  situation.  But  the  bradnal 
progress  of  science  gives  us  assurance  that  by  the  continued 
and  persistent  application  of  this  method — i.  e.,  by  treating 
phenomena  as  if  they  were  entirely  rational  and  entirely 
resembled,  at  least  in  principle,  our  mathematical  and  other 
models — we  can  worlc  our  way  towards  a  progressively  moru 
objective  and  more  complete  insight  into  the  nature  and  work- 
ings of  the  world  in  which  we  live. 

FOR  FURTHER   READING 

B.  Erdmai.*,  Logik,  (2nd  Edit.),  pp.  742-754,  774-784.  W.  R. 
Boyce  Gibson,  The  Problem  of  Logic,  pp.  326-327.  J.  G.  Htbben, 
Logic,  Part  II,  chapiter  1.  H.  Ixrtze,  Logic,  Bk.  II,  chapter  vll.  Chr. 
Slgwart,  Logic,  Vol.  II,  pp.  418-4W. 


; 


EXERCISES 

Point  out  the  necessary  Inter-relation  of  Inductive  and  deductive 
aspects  of  the  method  of  scientific  Investlsation  in  examining:  the 
following  cases:  il)  The  psycho-analytical  examination  of  a  hysteri- 
cal patient.  (2)  The  value  of  circumstantial  evidence  In  a  criminal 
case.  (3)  Testing  the  accuracy  of  a  chronoscope.  (4)  Studying  the 
eifectB  of  alcohol  upon  quantity  of  muscular  worit.  (5)  Licarning  to 
sing,  or  <to  play  upon  some  musical  Instrument.  (6)  Studying  bow 
far  Shakespeare  followed  the  details  of  his  "sources." 


CHAPTER  XXVIl 


W 

I     11' 


DEFINITION 

The  Problem.— What  are  our  habitual  belieis  on  the  subject 
of  definition?    In  the  first  place,  we  feel  sure  that  for  pur- 
poses of  clearness  in  exposition,  whether  In  discussion  or  In 
writing,  it  Is  well  to  have  the  exact  signlficatio-<  of  our  terms 
laid  down  beforehand,  and  to  use  our  terms  only  in  the  sense 
thus  established.     We  feel  that  language  is  misleading,  in 
that  one  and  the  same  word  Is  usually  associated  with  many 
meanings,  o,  ft,  c,  and  that  a  speaker  may  Intend  sense  a,  but 
the  hearer  may  understand  In  sense  ft  or  c.    The  misunder- 
standings which  thus  arise  are  sufficiently  annoying,  where 
they  are  not  merely  amusing,  in  ordinary  social  intercourse. 
But  In  scientific  discussions,  we  feel  sure,  such  variations  of 
meaning  are  not  to  be  tolerated.    Each  science  thus  tends  to 
develop  a  technical  language  of  its  own.  In  which  an  endeavor 
is  made  to  use  each  term  only  in  one  sense,  and  in  order  to 
have  It  known  what  that  sense  is.  it  is  usual  to  fix  It  by  an 
arbitrary  definition.     Carried  to  the  extreme  logical  conclu- 
sion to  which  this  feeling  of  ours  points,  science  should  estab- 
lish an  entirely  artificial  and  technical  system  of  signs— such 
as  we  find,  e.  g.,  in  algebra— in  order  to  express  its  thoughts 
in  a  v/ay  which  should  be  unmistakable.    That  is  to  say,  our 
feeling  for  the  necessity  of  clearly  defined  terms  leads  logic- 
ally to  the  creation  of  a  special  sclentitlc  language— to  what 
has  been  called  an  algebra  of  thought.     Among  thinkers,  a 
number  of  attempts  to  create  this  symbolic  language  have 
been  actually  made,  and  there  is  no  doubt  that,  with  all  their 
artificiality,  they  give  expression  to  a  natural  tendency  of  our 
thought  when  It  Is  dealing  with  problems  of  exposition.i 
In  the  second  place,  we  have  at  the  present  day  a  certain 

1  In  the  history  of  thouRht  this  attempt  Is  associated  especially 
,rlth  the  names  of  Itavmond  I-.illy.  and  of  I^lbnlj.  But  In  mode^m 
HmeH  «tmboU™loKic  flirulshea  an  excel!<-rt  oxamp  e.  aad  f"r  K-neral 
Dhlo^Dhk'al  purposes  the  construction  of  a  techn  cal  termiinoloBy  Is 
privo^ted  bv  ProfesW>r  Lovejov.  In  his  presidential  address  to  the 
AmerTcan  a'hilo^phni  Association.  See  PhUosophiral  Rnutc.  Vol. 
XXVI,  1917,  pp.  123-163. 

292 


NATURE  OF  DEFINITION 


i93 


mistrust  of  definitions,  even  in  the  more  abstract  and  tech- 
nical sciences.  We  thinlc  of  definition  as  somehow  interfering 
with  the  life  and  movement  of  thought,  as  crystallising  it  into 
clear-cut  forms  which,  with  all  their  clearness,  are  devoid  of 
life.  We  think  of  definition  as  somehow  implying  that  the 
movement  of  thought  has  come  to  an  end,  and  as  constituting 
a  check  upon  further  development.  It  is  unprogressive,  and 
stands  for  mental  stagnation.  We  think  of  it  as  a  creation 
of  mind  which  has  somehow  come  to  stand  between  us  and 
the  actual  phenomena  which  it  was  originally  designed  to 
represent — a  something  which  hinders  rather  than  aids  the 
pursuit  of  knowledge.  From  this  viewpoint,  then,  we  tend 
to  regard  exact  definitions  with  considerable  mistrust,  and  to 
feel  that  they  are  superficial.  They  may  be  clear,  but  they 
do  not  go  far  into  their  subject,  and  we  tend  to  regard  their 
function  as,  at  best,  provisional  only. 

There  is,  then,  in  our  ordinary  educated  thinking,  a  certain 
confusion  of  ideas  on  the  subject  of  definition.  On  the  one 
hand,  we  tend  to  view  it  as  extremely  valuable,  and  on  the 
other,  we  seem  to  regard  it  as  almost  harmful,  from  the  stand- 
point of  scientific  exposition  and  scientific  discovery.  The 
problem  of  the  present  chapter  is  to  study  the  subject  of 
definition  more  closely,  with  a  view  to  discovering  what  Its 
uses  are,  and  thus  to  remove  the  confusion  in  our  ordinary 
ways  of  thinking. 

Nature  of  Definition. — What  exactly  is  definition?  It  is  a 
statement  of  the  nature  of  some  subject  under  discussion.  In 
the  first  place,  it  is  a  statement,  a  mind-made  structure  or 
mental  model,  of  the  subject  of  discourse.  Thus  a  name,  or 
aay  sort  of  designation  which  is  fixed  by  the  mind  so  as  to 
refer  to  the  subject  of  discourse,  partakes  of  the  nature  of 
definition.  "The  subject  before  you  is  a  pencil.  It  is  used 
for  drawing  and  writing.  It  is  made  of  a  hollow  wooden 
cylinder  with  a  lead  core."  Each  sentence  here  contains  a 
different  sketch  or  mental  model,  and  is  so  far  to  be  regarded 
as  a  definition. 

In  the  second  place,  it  states  the  nature  of  a  subject.  It  is 
an  answer  to  the  question  "What  is  it?,"  or  "What  is  its 
nature?"  In  the  example  Just  given,  the  first  attempt  at 
definition  states  merely  that  it  is  a  thinkable  and  namable — 
i.  e.,  a  subject  of  discourse.  The  statement  of  the  name  does 
not  go  very  deeply  into  the  nature  of  the  pencil.    The  second 


294 


K 


DEFINITION 


attempt  defines  it  in  terms  of  use,  i.  e.,  treats  It  as  a  usable, 
or  as  something  whose  nature  is  to  be  understood  by  reference 
to  the  system  of  human  purposes.  Its  nature  is  declared  to  be 
instrumental.  It  is  a  tool  for  drawing  or  writing.  The  third 
attempt  defines  it  in  terms  of  the  material  out  of  which  It  is 
composed,  and  also  in  terms  of  structure— a  lead  core  sur- 
rounded by  a  wooden  cylinder.  These  are  three  attempts  to 
state  the  nature  of  the  object  in  question,  and  are  so  far 
definitions.  Let  us  take  another  instance.  "This  object  Is 
called  grass.  It  is  used  for  feeding  cattle— and  Indeed  for  a 
hundred  other  purposes.  For  the  botanist  it  is  one  thing,  for 
the  artist  it  is  another,  for  the  child  It  is  another,  and  for 
the  moralist  It  is  yet  another  thing.  It  is  not  made,  but  grows 
from  seed  in  the  following  way.  ...  It  belongs  to  the 
genus  called  poa.  It  is  a  mouocotyledon."  In  this  example, 
the  object,  not  being  an  artefact,  does  not  seem  to  have  a 
single  nature.  The  botanist  frames  one  mental  model  of  it, 
the  farmer  another,  and  the  moralist  yet  another.  And  there 
can  be  no  doubt  that,  from  his  special  viewpoint,  each  is 
justified. 

In  the  third  place,  it  is  some  subject  which  is  under  dis- 
cussion, which  we  define.  We  do  not  form  a  mental  model  of 
the  thing  as  it  exists  in  itself,  but  rather  of  some  aspect  of  It 
which  Interests  us.  In  fact  it  is  doubtful  how  far  objects  have 
what  we  could  call  a  "nature"  in  themselves.  What  we  define 
is  always  their  nature  in  reference  to  some  interest  or  purpose 
of  ours.  That  is  to  say,  our  definitions  have  not  only  an 
objective,  but  also  a  subjective  reference.  For  example,  it  is 
usually  possible,  given  a  number  of  definitions  of  one  and  the 
same  object,  to  infer  to  the  interest  or  purpose  behind  the 
definition.  Thus,  take  the  three  definitions  of  Grass:- (1)  the 
natural  food  of  sheep  and  oxen,  (2)  the  English  equivalent 
of  the  Latin  poa  pratensis,  (3)  a  species  of  the  genus  poo, 
tribe  festuceae,  family  gramineae.  It  is  easy  to  see  that  the 
first  is  a  farmer's  definition,  the  second  a  scholar's,  and  the 
third  a  botanist's  definition.  Definition,  then,  has  a  subjective, 
as  well  as  an  objective  reference. 

Aim  of  Definition  (A)  Objectivity.— Definition  thus  pre- 
sents us  with  a  mental  model  of  some  object  in  relation  to 
some  interest  of  ours.  What  is  our  aim  In  framing  such 
mental  models  or  statements?  In  the  first  plac  we  aim  at 
objectivity.     We  wish  to  represent  the  actual  nature  of  the 


AIM  OF  DEFINITION 


29S 


object  In  which  we  are  interested.     To  say  that  definition 
has  a  subjective  reference,  does  not  in  any  way  invalidate 
this  statement.     It  Is  true  that  it  is  from  his  own  point  of 
view  that  the  farmer  is  interested  in  grass.     But  from  that 
point  of  view  he  wants  to  know  what  grass  is.    The  point  of 
view  does  not  swallow  up  the  difference  between  natural  and 
artificial  feeds,  or  between  one  sort  of  feed  and  another.    On 
the   contrary,   the  special   viewpoint   leaus  to  special   refine- 
ments of  insight  into  the  nature  of  the  subject  under  dis- 
cussion—such as  studying  the  chemical  properties  of  grass 
which   render  it  especially   nutritive   to  cattle.     It   leads  to 
analysis  and   synthesis,   abstraction   and   determination,  and 
may  result  in  a  considerable  accession  of  Itnowledge.     So  too 
the  student  who  is  translating  from  Latin  into  English  does 
not  care  whether  poa  is  monocotyledonous  or  dicotyledonou. 
whether  sheep  feed  on  it  or  not— all  he  wishes  to  know  is 
by  what  English  word  it  is  best  translated.    But  this  he  does 
wish  to  know,  and  wish  to  know  correctly.     The  scholar's 
viewpoint,  too,  may  lead  to  all  kinds  of  refined  and  subtle 
research.     The   taking   a   special   viewpoint,   then,   does  not 
interfere  with  the  search  for  objectivity,  but  on  the  whole 
rather  assists  it  by  concentration  of  effort  in  a  special  direc- 
tion, and  we  can  fairly  say  that  our  primary  aim  in  defining 
is  objectivity,  or  getting  in  touch  with  the  real  nature  of  the 
object  under  discussion. 

(B)   Completeness.— In  the  second  place,  we  aim  at  com- 
pleteness.   We  aim  at  so  defining  or  stating  the  nature  of  the 
subject  of  discourse,  that,  from  the  viewpoint  which  interests 
us,  nothing  remains  to  be  added,  and  nothing  is  to  be  taken 
away.     Whatever  the  special  question  which  definition  asks, 
we  aim  at  answering  that  question  completely.    Thus  In  the 
case   of  poo  pratensis,   the   scholar's   "What   is   It?"   means 
what  is  Its  correct  English  name?,  and  the  complete  answer 
to  his  question  Is  contained  In  the  word  Meadow-grass.    What 
we  wish  to  avoid  in  definition   Is  vagueness,   indeflniteness 
ambiguity.  Incompleteness  In  any  shape  or  form.     We  war* 
to   be   definite,   precise,   exact,   clear,   final.     We   want   our 
definition  to  accomplish  what  it  sets  out  to  do.    We  want  it 
to  be  complete. 

How  Far  Reaiisabte?  (A)  With  Mind-made  Entities- 
How  far  can  we  express  the  nature  of  some  subject  in  which 
we  are  Interested,  in  a  way  which  shall  be  both  objective  and 


i;l 


296 


DEFINITION 


i 


III 


I!: 
llr 


complete?  Let  us  consider  flrat  the  case  of  mind-made 
entities.  "A  chair  is  a  piece  of  furniture  designed  for  a  single 
person  to  sit  on.  A  chair  is  made  of: — 4  legs,  with  supporting 
cross-pieces,  1  seat,  1  back,  and  possibly  1  or  2  arms.  These 
materials  are  put  together  in  such  a  way  that  the  legs  are 
fastened  to  the  seat  from  beneath,  and  the  arms  and  back 
from  above,  In  this  manner.  .  .  ."  Here  we  have  three 
definitions  of  a  mind-made  object  from  the  viewpoint  (1)  of 
function,  (2)  of  materials,  and  (3)  of  structural  plan.  All 
three  definitions  are  objective.  For,  in  spite  of  the  difference 
of  viewpoint,  each  expresses  the  actual  nature  of  the  object 
from  its  special  angle  of  approach.  Thus,  the  function  of  a 
chair  ia  to  be  sat  upon,  and  to  be  a  piece  of  furniture.  That 
is  what  Aristotle  would  call  its  final  cause,  the  idea  which  we 
seek  to  realise  in  constructing  chairs.  So  also  the  materials 
out  of  which  it  is  to  be  put  together  are  legs,  seat,  back,  etc., 
Just  as  much  as  the  "Two  N"a,  two  O'a,  an  L  and  a  D"  are  the 
materials  out  of  which  the  name  London  can  be  put  together 
This  is  what  Aristotle  callq  the  material  cause  of  the  chair. 
So  also  in  the  case  of  structural  plan.  If  the  materials  are 
put  together  in  accordance  with  the  directions,  we  do  actually 
have  a  chair.  This  is  what  Aristotle  calls  the  formal  cause. 
If  Aristotle's  viewpoint  i.s  here  accepted,  each  of  these 
definitions  will  be  seen  to  belong  to  the  causal  type  of  mential 
model,  though,  in  respect  of  the  last  two,  mathematical 
aspects  also  enter  in.  In  dealing,  then,  with  artefacts,  our 
definitions  can  be  objective. 

Can  they  also  be  complete?  "A  piece  of  furniture  designed 
for  a  single  person  to  sit  upon" — <s  this  a  complete  definition 
of  a  chair?  Complete,  that  is,  from  its  special  standpoint? 
We  can  test  its  completeness  by  asking  (1)  are  all  chairs 
pieces  of  furniture  designed  with  this  purpose,  and  (2)  are 
all  pieces  of  furnitu.'-e  designed  for  a  single  person  to  sit 
upon — chairs?  (1)  seems  to  be  correct  enough,  but  (2)  seems 
to  Include  stools  as  well  as  what  we  should  call  chairs. 
However,  If  what  we  are  interested  in  is  not  structure,  but 
function,  even  (2)  is  correct.  For  the  difference  between  stool 
and  chair  is  chiefly  structural.  From  the  special  viewpoint, 
then  which  is  Interested  in  function,  our  definition  may  be 
regarded  as  complete.  So  too  in  the  case  of  the  other  two 
definitions.     (1)   All  chairs  are  constructed  out  of  m.  terial 


AIM  OF  DEFINITION 


297 


Buch  as  leg8,2  a  seat,  a  back,  and  poulbly  arms,  and  (2)  all 
objects  constructed  of  such  materials  are  what  we  should  call 
chairs.  So  too  (1)  all  chairs  are  constructed  in  accordance 
with  the  plan  mentioned,  and  (2)  all  objects  constructed  in 
accordance  with  such  a  plan  would  be  called  chairs.  In  deal- 
ing with  artefacts,  then,  our  definitions  can  be  regarded,  not 
only  as  objective,  but  also  as  complete,  at  least,  from  the 
special  standpoint  of  each  definition. 

Let  us  take  another  example.  "A  triangle  is  what  one  learns 
to  construct  in  a  special  form  in  the  first  proposition  of  the 
first  book  of  Euclid.  A  triangle  is  a  three-sided  rectilineal 
closed  figure.  A  triangle  consists  of  three  angles  which 
together  form  a  closed  figure.  A  triangle  is  a  rectilineal 
closed  figure,  the  internal  angles  of  which  are  together  equal 
to  two  right  angles.  A  triangle  is  a  rectilineal  closed  figure 
such  that  any  one  of  its  external  angles  is  equal  to  the  sum 
of  the  interior  opposite  angles.     Etc.,  etc." 

Each  of  the  above  definitions  is  objective.  The  construction 
of  a  triangle  is  the  subject  treated  of  in  Euclid  I.  I,  a  triangle 
ia  a  three-sided  figure,  a  three-angled  figure,  and  does  possess 
all  the  other  properties  ascribed  to  it,  along  with  very  many 
more  which  might  equally  well  have  been  used,  and  no  doubt 
many  of  which  have  not  yet  been  discovered.  Of  the  objec- 
tivity of  ail  of  these  definitions,  there  can  be  no  possible 
doubt.     Are  they,  however,  all  complete?     Let  us  consider? 

(1)  All  triangles  are  what  we  learn  to  construct  in  a  special 
form  in  Euclid  I.  1.— Yes,  for  we  there  do  learn  to  construct 
the  equilateral   form,  to  construct  any  equilateral   triangle. 

(2)  All  things  which  we  learn  to  construct  in  the  special  form 
according  to  Euclid  I.  i,  are  triangles.— Yes,  this  also  is  true. 
All  equilateral  triangles  are  certainly  triangles.  The  first 
definition,  then,  appears  to  be  complete.  Again,  (1)  all 
triangles  are  three-sided  rectilineal  closed  fiKuves,  :>nd  (2)  all 
three-sided  rectilineal  closed  figures  are  triangles.  The  second 
definition  Is  complete,  and  the  same  proves  to  l?"  the  case 
when  we  apply  the  same  test  to  the  others!  If  vne  above 
examples  may  be  regarded  as  typical,  then,  we  can  state  that 
in  respect  of  mind-made  entities  our  definition  can  be  both 

2  The  number  of  legs  Js  relatively  Immaterial.  We  think  of  most 
chairs  as  possessing  four  legs.  If,  however,  It  Is  thought  advisable 
to  point  out  that  some  chairs  have  only  three  legs,  and  are  still  oerfect 
as  chairs,  It  la  easy  to  alter  the  definition,  by  specifying  tte  Doislble 
variation  In  the  number  of  legs,  as  of  arms.        ''»"'"'y"'8  "»e  possioie 


If 


?  'I 


296 


DKFINITION 


■ 

i 


If 


m. 


\w 


objective  and,  from  iU  special  viewpoint,  complete.  This  Ig 
egpeclally  recognised  In  the  case  of  equations.  An  equation 
Is  recognised  as  the  complete  definition  of  the  corresponding 
graph,  and  the  corresponding  graph  might  equally  well  be 
regarded  as  the  complete  definition  (from  a  certain  viewpoint) 
of  the  equation.:! 

(B)     With    Natural    Phenomena.— As    we   have    seen,   we 
deal  with  natural  phenomena  through  the  medium  of  mental 
models,  and  thus  our  definition  of  a  natural  phenomenon  is 
the  mental  model  itself,  in  terms  of  which  we  are  trying  to 
understand  the  phenomenon  in  question.    As  there  is,  further, 
a  gap  which   separates  our  mental  model  from  the  natural 
phenomenon,  there  can  be  no  doubt  that  our  definitions  are, 
directly,  statements  of  something  different  from  the  object  to 
be  defined,  and  refer  to  the  object  itself  only  indirectly.    Thus, 
when  we  define  an  island  as  "a  piece  of  land  surrounded  by 
water,"  we  are  directly  constructing  the  mental  model  of  a 
circle — or  of  some  such  geometrical  outline— and  we  can  only 
apply   this  mathematical  model  to  the  natural  phenomenon 
by  a  kind   of  mental   /lot- "Let  one  side  of  this  figure  be 
regarded  as  land,  and  the  other  as  water."    If  we  change  the 
direction  of  this  flat,  and  regard  the  outside  as  land,  and  the 
inside  as  water,  we  have,  with  the  same  geometrical  model, 
the  definition  of  a  lake.    At  the  same  time,  although  there  is 
thus  a  gap  between  the  mental  model  and  the  reality— a  gap 
which   has  to   be   bridged   by   this  flat,   a   certain   degree  of 
objectivity  cannot  be  denied  to  such  definitions.    If  we  define 
an  island  as  "a  hill-hop  from  the  sea-floor  projecting  in  part 
above  the  water-level,"  we  seem  to  be  a  little  more  nearly 
expressing  Its  objective  nature.    So  too  in  Zoology  it  is  usual 
to  define  the  spider  or  the  horse  in  terms  of  the  mental  model 
of    fa-nlly    relationship.      In    such    cases,    while   there    is   no 
doubt  that  this  specific  model  has  an  objective  application, 
reference  to  a  number  of  authorities  will  show  that  opinions 
differ  as  to  what  animals  should  be  assigned  to  the  arthropod 
or  mammal  group,  and  even  to  the  invertebrate  and  vertebrate 
groups.     From  this  evidence  it  would  appear,  that,  so  far  as 
the  concrete  filling  in  of  this  mental  model  is  concerned,  we 
can  hardly  expect  full  objectivity.     Still,  there  is  no  doubt 
that  such  deflnltloiis  are  partly  objective,  and  that,  as  science 


3Cf.  Goblot,  Tralti  de  Logiquc,  pp.   121-122. 


TYPES  OF  DEFINITION 


299 


advances,  definition  of  natural  phenomena  can  become  progre»^ 
■ively  more  objective. 

So  also  lu  respect  of  completeness.  The  work  of  science  li 
never  complete,  and  consequently  the  summing  up  of  our 
knowledge  at  a  definite  stage,  and  Its  embodiment  In  a  defini- 
tion, can  never  be  fully  complete.  In  respect  of  completeness, 
then,  as  well  as  of  objectivity,  the  aim  of  definition  can  in 
such  cases  be  only  approximately  and  progressively  realised. 

Types  of  Definition.— The  general  question  of  definition 
is  "What  is  it?"  To  this  question  certain  typical  forms  of 
response  are  given  by  certain  typical  forms  of  definition. 
Let  us  consider  a  few  of  the  more  prominent  forms.  In  the 
first  place,  definition  means,  laying  down  the  flne$  or  boond- 
arles  of  a  subject,  establishing  its  outlines  in  such  a  way  as 
to  distinguish  It  from  all  other  subjects  with  which  it  might 
be  confused.  For  example,  "Pages  387-419  of  Pillsbury'i 
Fundamentals  of  Paychology"  is  an  exact  preliminary  defini- 
tion of  an  assignment  on  the  subject  of  Reasoning— a  state- 
ment of  the  boundaries  of  the  subject  to  be  studied,  which  la 
perfectly  adequate  to  distinguish  it  from  being  confused  with 
any  kindred  subject.  So  too,  "all  books  numbered  160-199"  is 
an  exact  preliminary  definition  of  the  books  on  philosophy  in 
the  Minnesota  University  library.  It  lays  down  the  precise 
boundaries  within  which  such  books  will  be  found,  and  serves 
to  distinguish  philosophy  books  from  books  on  psychology— 
which  are  numbered  150-159— with  all  the  precision  to  be 
expected  in  a  library.  For  assistants  in  the  library,  and  for 
such  students  as  have  access  to  the  stacks,  such  definitions  are 
not  only  useful,  but  also  fdr  many  purposes  perfectly  adequate. 
For  certain  purposes  they  are  not  only  needed,  but  are  all 
that  is  needed. 

What  exactly  is  this  kind  of  definition?  It  is  not,  of  course, 
the  object,  but  Is  rather  a  kind  of  outline  sketch  or  model  of 
its  boundaries.  It  is  even  of  a  mathematical  character,  and 
indeed  derives  much  of  its  exactness  from  the  use  of  numbers. 
Its  function  is  to  localise  the  object  with  which  we  wish  to 
get  in  touch,  and  it  has  even  a  directly  spatial  reference. 
This  is  true  not  only  In  such  cases  as  "The  third  house  on 
your  right  after  you  have  crossed  the  park,"  as  a  definition 
of  the  locality  where  Mr.  X  lives,  but  also  of  the  portion  of 
the  text-book  set  for  a  lesson  on  Reasoning,  and  even  in  the 
case  of  the  philosophy  books — for  the  numbers  have  a  very 


300 


DFCFINITION 


It 


definitely  spatial  reference  to  certain  ahelvea  located  In  a 
ceruin  room  of  the  library.  Such  a  definition  tells  ui.  not 
exactly  what  the  object  U.  but  rather  where  It  U  to  be  found. 
It  Ih  a  mathematical  model  with  a  spatial  reference. 

Let  us  consider  a  second  type  of  definition.  "A  pencil  Is 
something  used  for  writing,  when  there  Is  no  Ink.  A  type- 
writer Is  something  you  use  when  you  want  to  write  as 
clearly  as  print.  A  spoon  Is  something  you  use  for  stirring 
liquids,  or  for  eating  food  like  soup  or  oatmeal.  A  meal  Is 
what  you  take  to  satisfy  hunger.  A  dog  Is  what  you  use  to 
guard  the  house  from  tramps.  Art  and  religion  are  the  most 
ennobling  things  we  have  In  life."  For  certain  purposes, 
especially  practical  purposes,  there  can  be  no  doubt  that  such 
definitions  are  perfectly  adequate.  They  are  sketches  of  the 
objects  in  terms  of  u»c,  and  thus  refer  partly  to  the  nature 
of  the  object,  and  partly  to  the  system  of  human  purposes. 
On  the  one  hand,  they  tell  us  what  the  object  can  be  used  for, 
and  on  the  other,  they  tell  us  how  we  can  use  it.  They  are 
thus  mental  models  of  the  objects  under  discussion,  in  terms 
of  human  uses,  and  as  such  are  of  the  greatest  importance  to 
practical  men. 

There  are  many  other  types  of  definition.  Thus,  certain 
definitions  refer  less  to  what  we  human  beings  can  do  with 
the  object,  and  more  to  what  It  itself  does  In  a  state  of 
nature: — "A  fire  is  something  which  bums.  Water  is  some- 
thing which  flows,  and  wets  whatever  falls  Into  it.  H.  i  ■  is 
something  which  comes  down  from  clouds  in  the  form  of 
drops  of  water— is  something  which  helps  to  make  the  crops 
grow,  especially  In  the  spring-time."  This  Is  a  kind  of  causal 
model,  and  tells  us  what  the  object  does.  Another  type  of 
■  causal  model  tell  us  rather  how  an  object  Is  caused  or  pro- 
duced:— "Thunder  is  a  phenomenon  due  to  lightning.  Plant- 
rust  is  a  phemonenon  due  to  the  action  of  bacteria.  A  rain- 
bow is  a  phenomenon  caused  by  our  seeing  the  sunlight 
through  water." 

The  typical  forms  of  definition  meet  the  general  question 
"What  is  it?"  by  answering  questions  such  as  "Where  is  it. 
What  can  we  do  with  it,  W'hat  does  it  do,  or  make,  or  cause. 
How  is  it  caused,  or  made,  or  produced.  What  is  it  made  of. 
What  is  its  law  nr  principle  of  construction?"  There  is  no 
limit  to  these  questions.  Each  expresses  a  different  interest, 
or  represents  a  different  angle  of  approach,  and  there  are  as 


VALIDITY  OF  DKFINITION 


301 


many  posiible  typ«ii  of  deflnitlon  an  there  tire  ponaible  inter- 
ests, or  possible  questions  to  be  asked.  As  these  are  Indefi- 
nite In  number,  and  have  never  beci*.  classitled.  It  it  profltleM 
to  attempt  to  limit  definition  to  any  one  'orm — aa  has  been 
attempted  in  the  history  of  logic.  Any  definition  which 
answers  Its  special  question  in  a  way  which  Is  objective  and 
reasonably  complete,  represents  a  legitimate  type  of  defini- 
tion, and  no  deflnitlon  absolutely  exhausts  the  full  nature  of 
its  subject. 

Validity  of  Definition.— Definitions  are  mind-made  entities 
in  terms  of  which  we  try  to  understand  the  world  around  ua. 
There  Is  thus  something  experimental  about  them.  They 
enter  into  the  method  of  trial  and  error,  and  are  frequently 
mistaken  and  thus  false.  In  point  of  fact,  this  is  true  when 
we  are  defining  mental  models  themselves,  as  well  as  in  the 
case  of  natural  phenomena.  Thus,  a  common  dictionary  defi- 
nition of  a  triangle  is  "A  figure  with  three  angles."!  But  if  we 
test  this  by  asking,  are  all  figures  with  three  angles  triangles? 
we  see  at  once  that  It  Is  Inadequate.  For  we  might  have  an 
open  figure,  like  a  square  with  one  corner  missing — which 
would  certainly  be  a  figure  with  three  angles,  and  would  with 
equal  certainty  not  be  a  triangle.  So  too  a  common  dictionary 
deflnitlon  of  chair  Is  '"A  movable  seaf'i  But  strip  a  chair  of 
its  legs  and  back,  and  It  is  stlU  a  movable  seat.  So  also  a 
stool  or  bench  might  be  called  a  movable  seat.  But  none  of 
these  would  be  called  chairs.  In  the  tase  of  nutu.'-al  phenom- 
ena, it  Is  not  necessary  to  give  specific  Instances.  For  as  the 
history  of  science  shows,  all  definitions  of  such  phenomena  are 
Incomplete,  and  very  many,  if  not  all,  are  also  partially  false. 
Definitions,  then,  may  be  invalid.  On  what  does  their  validity 
or  invalidity  depend? 

In  the  case  of  mind-made  entities,  where  the  object  may  be 
created  by  mental  construction.  It  is  possible  for  a  definition 
to  be  perfectly  valid.  Thus  we  can  define  the  knight's  move 
or  bishop's  move  in  class  with  perfect  accuracy,  or  "Align- 
ment" and  "Point  of  rest"  in  military  science,  provided  that 
we  follow  the  established  conventions.  So  also  In  the  case  of 
triangles  and  other  mathematical  objects.  If  we  accept  the 
general  view  of  mathematical  space,  w^e  can  define  with  suffi- 
cient accuracy.    Mistakes  are  made  here  from  time  to  time,  but 

1  The  definitions  here  are  taken  from  The  American  Popular  Die- 
Honary  of  the  Enftlish  Languaoe. 


j; 


302 


DEFINITION 


m 


they  can  be  rectified,  and  made  satisfactory  in  point  of  objec- 
tivity and  completeness.  In  the  case  of  natural  phenomena, 
however,  complete  validity  Is  out  of  the  question.  But  our 
definitions  can,  even  in  such  cases,  approximate  to  validity  as 
scientific  knowledge  increases,  and  as  our  definition  sums  up 
correctly  the  knowledge  of  our  own  time.  The  only  adequate 
test  of  such  definitions  is  the  progress  of  science  itself.  The 
further  development  of  knowledge  alone  can  show  whether 
the  views  held  at  an  earlier  stage  were  pointed  in  the  right 
direction  or  not.  In  general,  then,  a  definition  is  valid,  so 
far  as  from  its  special  viewpoint  It  expresses  the  objective 
nature  of  the  phenomenon  under  discussion. 

Function  of  Definition  in  Exposition. — For  scientific  pur- 
poses, whether  of  inquiry  or  of  exposition,  definition  has  two 
main  functions.  In  the  first  place,  it  is  used  in  opening  up 
an  inquiry,  in  the  form  of  a  preliminary  definition.  Its  use 
in  such  cases  is  to  establish  the  general  lines  along  which 
research  or  discussion  is  to  be  carried  on.  Thus,  in  scien- 
tific exposition,  it  is  usual  to  start  with  a  statement  of  the 
"problem,"  or  to  sum  up  the  beliefs  with  which  we  approach 
a  new  subject,  as  Coleridge,  before  opening  &  nex  book,  used 
to  write  down  briefiy  his  own  thoughts  on  the  subject.  Used 
in  this  way,  preliminary  definitions  are  found  very  helpful 
in  dealing  clearly  and  objectively  with  a  subject  of  discourse. 

In  the  second  place,  definition  is  used  in  closing  an  inquiry, 
in  the  form  of  a  concluding  or  final  definition.  In  such 
cases  its  function  is  to  sum  up  the  results  of  inquiry,  to 
answer  the  problem  set  at  the  beginning,  or  at  least  to  sum  up 
the  beliefs  with  which  we  lay  the  subject  on  one  side — as 
Dome  thinkers  write  down  briefly  what  they  have  learnt  from 
each  book  they  read,  immediately  after  finishing  it.  Such 
concluding  definitions  are  of  the  utmost  value  in  promoting 
clearness,  definiteness,  and  objectivity  in  our  researches  and 
explanations. 

Summary  and  Conclusion. — So  far  we  have  seen  that  defini- 
tion states,  in  terms  of  some  mental  model,  the  nature  of 
some  subject  of  discourse,  and  that  its  aim  is  objectivity  and 
completeness.  This  aim  can  be  attained  in  the  case  of  mind- 
made  entities,  and  we  can  at  least  progressively  approximate 
to  such  objectivity  and  completeness  in  the  case  of  natural 
phenomena.  We  have  also  seen  that  the  chief  use  c'  ni- 
tion  in  scientific  exposition  is  to  open  or  close  an  im    u      in 


VALUE  OF  DEFINITION 


303 


the  form  of  a  preliminary,  or  of  a  c  deluding  definition,  as 
the  case  may  be. 

We  should  now  be  In  a  position  to  resolve  the  difficulty 
with  which  our  Inquiry  opened.  Is  definition  a  help,  or  is 
It  a  hindrance,  to  scientific  progress?  It  Is  certainly  a  crea- 
tion of  mind,  a  mental  moid,  but  its  function  is  not  to  stand 
between  us  and  the  objec  .  and  thus  obs.ture  or  mislead  our 
vision.  Its  aim  is  to  sta  the  nature  ff  the  object,  and  to 
be  a  help  towards  cleariii  -  up  our  Ideas  and  guiding  our 
vision  aright,  and  we  can  state  that,  li:  proportion  as  mental 
models  prove  of  assistance  to  the  progress  of  knowledge,  so 
far  definitions  are  helpful.  On  the  whole,  the  preliminary 
definition  seems  of  more  assistance  than  the  concluding 
definition — for  it  certainly  leads  to  further  progress.  But  if 
we  adopt  the  modern  progressive  view  of  science,  and  do  not 
regard  our  conclusion — the  summing  up  of  our  Inquiries  as 
far  as  we  have  gone— aa  concluding  the  subject,  and  exhaust- 
ing the  nature  of  the  subject  Itself,  we  can  say  more.  If  we 
regard  our  concluding  definition  not  as  in  any  way  final,  but 
rather  as  leading  on  to  more  determinate  inquiries,  both  forms 
of  dehcitlon  may  be  equally  fruitful  and  equally  helpful  In 
scientific  exposition.  What  we  objected  to  in  definition,  was 
not  its  clearness  but  Its  tendency  to  pass  over  into  dogmatism. 
Into  the  idea  that  it  was  more  than  an  experimental  mental 
model,  always  subject  to  revision.  If,  however,  we  avoid  this 
error,  we  shall  find  definition  always  of  assistance  in  under- 
standing ourselves  and  in  general  the  world  in  which  we  live. 

FOR  FURTHER  READING 

W.  R.  noyce  Gibson,  Tfffe  Problem  of  Logic,  pp.  32-36.  H.  T>otze, 
Logic.  Bk.  II.  chapter  i.  Chr.  Slgwart.  Logic.  Vol.  I.  pp.  286-294! 
W.  Wundt,  Logik.  (3rd  EJdlt.).  Vol.  II.  pp.  40-47. 


EXERCISES 

1.  Give  three  definitions  of  each  of  the  following,  from  thre« 
different  viewpoints :  Circle,  Typewriter,  Child,  Apple,  Air-plane, 
Diamond.   Dandelion,   Book,   Ink,  Student. 

2.  Is  there  any  viewpoint  from  which  the  following  definitions  ire 
strictly  legitimate;  (a>  A  lake  Is  a  water  Island  .n  the  land,  (b) 
A  lama  is  a  wooHy  sort  of  fleecy  hairy  goat,  with  an  Indolent  expres- 
sion and  an  undulating  throat,  (c)  A  liar  Is  a  man  who  wilfully 
misplaces  his  ontolocloal  predicates,  (d)  A  caterpillar  Is  an  emblem 
of  life  and  a  vision  of  Joy.     (e)  A  straight  line  Is  the  arc  of  a  circle 


304 


DEFINITION 


of  infinite  radius,  (f)  A  useless  life  Is  a  form  of  death,  (g)  God 
is  a  substance  consisting  In  infinite  attributes,  of  wliicb  each  expresses 
eternal  and  infinite  essentiality,  (h)  True  wit  is  nature  to  advantage 
dressed,  what  oft  was  thought,  but  ne'er  so  well  expressed,  (i)  A 
politician  is  not  a  saint.  (J)  A  locomotive  is  something  which  moves 
from  one  place  to  another,  (k)  An  honest  man  is  the  noblest  worli 
of  God.     (1)   Architecture  is  frozen  music? 


bf 


|I> 


rn 


CHAPTER  XXVIII 


CLASSIFICATION 


The  use  of  classification  is  universal.  Not  only  In  science, 
but  also  in  every-day  life,  we  classify  everything  and  every- 
body. We  classify  a  new  acquaintance  as  someone  we  can 
or  cannot  get  on  with.  We  classify  him  as  clever,  stupid,  or 
just  average.  We  classify  him  as  old,  young,  or  middle-aged 
— as  tall  or  short,  thin  or  fat,  plain  or  good-looking,  rich  or 
poor.  In  fact,  there  is  no  viewpoint — social.  Industrial,  politi- 
cal, artistic,  religious,  etc.,  from  which  we  cannot  put  him 
into  some  class,  into  a  group  along  with  other  people.  In 
science,  the  importance  of  classification  for  investigation,  as 
well  as  for  exposition,  can  hardly  be  over-estimated.  By 
grouping  together  a  large  number  of  phenomena  or  experi- 
ences which  bear  upon  a  single  point,  it  is  usually  possible 
for  a  scientist  to  obtain  insight  into  some  law,  or  for  a 
speaker  or  writer  to  transmit  his  own  insight  to  others.  In 
general,  then,  for  every-day  life  as  for  science,  classification 
is  of  univt.rsal  use. 

Nature  of  Classification. — Just  what  is  classification?  It 
means,  quite  simply,  patting  together  so  as  to  form  a  class. 
In  the  first  place.  It  signifies  our  putting  together.  That  Is  to 
say,  the  viewpoint  from  which  we  classify  is  ours,  depends 
upon  our  interests  and  purposes,  and  is  so  far  subjective  and 
even  arbitrary.  For  instance,  to  group  together  books  on 
various  subjects,  in  accordance  with  the  first  letter  of  the 
writer's  surname,  seems  thoroughly  artificial.  It  has  very 
little  to  do  with  the  nature  of  the  book,  and  indeed  seems 
largely  accidental.  There  Is  no  logical  connection  between  the 
fact  that  this  book,  which  happens  to  je  on  metaphysics, 
should  have  been  written  by  a  man  whose  family  name  began 
with  M,  and  the  fact  that  that  book,  which  happens  to  be  on 
metaphysics,  should  have  been  written  by  a  man  whose  family 
name  began  with  B  or  T.  There  is,  in  fact,  no  necessary  connec- 
tion between  the  first  letter  of  a  man's  surname  and  the  nature 
of  his  writings.   Why,  then,  do  we  group  books  in  this  way? 

305 


U: 


306 


CI.ASSIFICATION 


i 


It  is  because  we  And  It  convenient.  There  are  only  twenty- 
six  letters  in  the  alphabet  we  use,  and  we  are  thus  able  t 
assign  any  book  whatever  to  some  one  of  twenty-six  recog 
nised  classes,  and  for  purposes  of  reference  this  Is  found 
convenient.  So  too  in  a  very  small  private  library,  it  Is 
quite  common  to  find  books  assigned  to  different  shelves  In 
accordance  with  their  size,  so  that  all  the  smaller  volumes 
go  on  this  shelf,  and  all  the  ponderous  tomes  on  that.  This 
also  has  little  or  nothing  to  do  with  the  contents  of  the 
books  In  question,  but  it  suits  the  conveniences  of  the  owner 
of  the  books.  So  too  for  purposes  of  shipping,  books  can  be 
classified  according  to  weight,  or  for  esthetic  purposes  accord- 
ing to  color  and  style  of  binding.  They  might  also  be  classi- 
fied according  to  place  of  publication,  according  to  date  of 
publication,  according  to  the  name  of  the  publisher — or  accord- 
ing to  any  one  of  a  hundred  different  interests  and  purposes. 
Classification,  then,  in  the  first  place  is  arbitrary.  We  put 
together  in  accordance  with  our  interests. 

To  this  arbitrariness  there  Is,  however,  a  limit.  "We  put 
together  only  what  can  be  put  together.  We  do  not  group 
books  according  to  their  thermodynamic  qualities,  or  accord- 
ing to  their  arboreal  habits,  or  according  to  their  qualities  as 
chronoscopes,  plethysmographs,  or  type-writers — because  they 
have  no  such  qualities.  We  put  them  together  In  accordance 
with  characteristics  which  they  really  have.  It  may  be  acci- 
dental for  a  book  on  political  economy  to  be  written  by  a 
man  whose  family  name  began  with  M.  There  are  books  on 
political  economy  written  by  men  whose  names  began  with 
S  or  V.  But  there  is  no  doubt  that,  in  that  particular  case. 
It  does  begin  with  M,  and  as  we  find  that  convenient  for  our 
purposes,  we  make  use  of  that  characteristic.  In  the  second 
place,  then,  we  group  together  In  accordance  with  some  char- 
acteristic which  the  object  to  be  classified  really  possesses. 

In  the  third  place,  we  put  them  together  so  as  to  form  a 
class.  What  is  a  class?  A  class  is  a  group  of  Individuals 
held  together  by  some  law  of  connection,  this  law  being  some 
principle  which  all  have  in  common.  Thus  students  of  biology 
form  a  class,  being  held  together  by  the  Interest  In  biology 
which  all  have  in  common.  Books  written  by  men  whose  sur- 
names begin  with  M  form  a  class,  being  held  together  by  the 
characteristic  which  all  possess  In  common,  and,  In  general, 
wherever   objects   have   a   single   characteristic  in  common, 


a.  il 


AIM  OF  CLASSIFICATION 


307 


whatever  that  characteristic,  and  however  superficial  or  acci- 
dental It  may  seem,  such  objects  can  be  grouped  together 
so  as  to  form  a  class,  provided  always  that  some  one  happens 
to  be  Interested  In  that  special  characteristic. 

Finally,  In  order  to  obtain  a  clear  idea  of  the  nature  of 
classification,  we  must  compare  it  with  what  is  known  as 
Division.  Classification  groups  together  individuals  so  as  to 
form  a  class.  Division  takes  a  class  apart,  so  as  to  form  mb- 
classes.  Thus,  we  can  group  individuals  together  as  Amer- 
icans, as  men  Interested  in  business,  as  millionaires,  as 
politicians,  or  simply  as  men.  This  is  classification.  On  the 
other  hand,  we  can  take  the  class  men,  and  subdivide  it  Into 
white-skinned,  yellow-skinned,  brown-skinned,  red-skinned 
men,  etc.,— i.  e.,  we  can  divide  the  class  up  into  sub-classes 
according  to  variations  in  respect  of  a  single  characteristic. 
So  too  we  can  divide  politicians  into  progressives  and  reaction- 
aries, into  honest  and  corrupt,  or  millionaires  into  coal-kings, 
railroad-kings,  etc.,  according  to  variations  in  respect  of  the 
source  of  their  wealth.  On  the  whole,  division  and  classifica- 
tion should  be  regarded  as  two  aspects  of  a  single  method,  like 
analysis  and  synthesis,  abstraction  and  determination,  etc., 
and  In  order  to  grasp  sufficiently  the  nature  of  classification! 
it  is  necessary  to  bear  in  mind  this  relation  to  division.  Thus,' 
in  classifying  individuals  as  millionaires,  we  are  putting  them' 
Into  what  is  a  sub-dlvlslon  of  the  class  men,  and  In  dividing 
the  class  milUonaires  into  the  sub-classes  of  coal-kings,  rail- 
road-kings, etc.,  we  are  forming  classes.  Classification  thus 
means,  placing  individuals  together  in  a  class  which  is  usually 
Itself  to  be  regarded  as  a  sub-class  of  some  wider  organisa- 
tion. 

Classification,  then,  Is  arbitrary— In  that  a  claat  is  formed 
from  some  particular  viewpoint;  yet  not  wholly  arbitrary— 
for  the  Individuals  which  are  put  Into  the  class  all  possess 
some  common  characteristic.  In  virtue  of  which  they  can  be 
unified  and  regarded  as  constituting  a  single  group;  and 
finally  the  class  which  we  form  is  usually  a  part  of  some 
wider  system,  so  that  classification  is  a  kind  of  organisation. 

Aim  of  Classification  (A)  Objectivity.— What  do  we  classify? 
What  is  our  aim  In  grouplns:  together  all  sorts  of  objects 
which  possess  a  single  characteristic  In  common?  In  the 
first  place,  we  aim  at  objectivity,  it  is  with  a  view  to  hand- 
ling  the  objects  more  conveniently,   and  understanding  the 


308 


CLASSIFICATION 


objects  more  readily,  that  we  form  them  Into  groups.  Every 
science,  and  every  complex  research  or  exposition,  has  its 
classlflcatory  stage,  during  which  It  is  assembling  material 
and  getting  It  into  usable  shape.  It  is  with  the  aim  of  getting 
into  closer  touch  with  the  objective  nature  of  this  material, 
that  science  classifies  it,  or  forms  it  into  various  groups  whIcE", 
for  purposes  of  inquiry  or  exposition,  seem  to  belong  together. 
Thus  in  Botany,  the  otherwise  enormous  and  imwieldy  mass 
of  material  is  grouped  according  to  the  family  connections 
of  the  different  small  groups,  so  that  the  plan  of  systematic 
botany  resembles  a  genealogical  tree.  But  this  classification, 
which  is  made  primarily  from  the  viewpoint  of  the  evolution- 
ary theory,  is  in  a  secondary  way  of  use  for  other  purposes 
also,  so  far  as  it  makes  the  material  more  easily  handled. 
Thus,  in  studying  the  reactions  of  plants  to  stimulation,  the 
new  viewpoint  cuts  across  all  the  old  class  distinctions,  and 
it  is  necessary  to  form  an  entirely  new  grouping,  according  as 
the  type  of  reaction  to  light,  for  Instance,  or  to  contact,  sep- 
arates members  of  one  and  the  same  family  group,  and  links 
them  up  with  members  from  widely  diverse  branches  of  the 
genealogical  tree.  But  until  the  re-grouping  in  accordance 
with  the  new  interest  has  been  effected,  it  is  found  conveni- 
ent to  investigate  one  family  group  at  a  time,  in  search  of 
the  new  characteristics,  following  through  the  standardised 
family-group  plan,  until  the  whole  ground  has  been  covered. 
So  too  with  periodical  literature.  It  is  published  in  various 
magazines,  each  of  which  for  purposes  of  reference  tends  to 
be  regarded  as  forming  a  kind  of  standardised  class  of  its 
own.  But  when  we  are  interested  in  some  single  question — 
e.  g.,  the  study  of  apparitions — we  collect  together  into  spe- 
cial groups  all  articles  dealing  with  apparitions  of  animals, 
apparitions  of  mail-coaches,  apparitions  of  houses  and  gar- 
dens, etc.  But  until  the  new  grouping  has  been  carried 
through,  we  find  it  convenient  to  make  use  of  the  old  group- 
ing in  magazine-units,  because  in  this  way,  by  looking  up 
the  index  of  magazine  A,  of  magazine  B,  etc.,  we  can  conveni- 
ently cover  the  whole  ground,  and  can  get  into  touch  with 
everything  in  the  periodical  literature  which  bears  on  our 
special  interest.  The  primary  aim,  then,  of  classification  is 
to  reduce  the  material  studied  to  such  a  form  that  we  can 
handle  it  conveniently,  and  thus  bring  ourselves  into  closer 


AIM  OF  CLASSIFICATION 


309 


contact   with   the   objective   facts   than   would   otherwise   be 
possible. 

(B)  Completeness. — In  the  second  place,  we  aim  at  a  cer- 
tain kind  of  completeness.  We  wish  to  cover  the  whole  ground, 
and  to  leave  nothiag  important  out  of  account.  Classification 
and  division  together  always  aim  at  covering  the  entire  field. 
Division,  for  Instance  always  tries  to  be  exhaustive.  We 
divide,  e.  g.,  books  In  general  into  books  on  history,  books  on 
chemistry,  books  on  philosophy,  etc.,  and  at  the  end,  when  we 
have  used  up  all  the  definite  subjects  of  study  or  reference, 
we  group  together  the  remaining  volumes  as  "miscellaneous." 
So  too  in  classifying.  If  we  are  making  a  collection  of  all 
books  bearing  upon  some  minute  point  in  history  or  literature, 
or  on  a  subject  such  as  porcelain  or  indigo-dyeing,  we  want 
our  class  to  be  complete.  In  such  cases,  in  order  to  ensure 
that  nothing  important  shall  escape  us,  we  tend  to  go  over 
the  whole  ground  by  the  aid  of  division,  so  that  all  standard 
groups  of  books — literature,  history,  art,  etc. — come  In  for 
consideration,  and  the  whole  field  of  literature  is  covered. 
We  do  not,  of  course,  aim  at  including  every  single  book  bear- 
ing on  our  subject,  but  rather  one  book  for  each  distinctive 
view  point,  i.  e.,  at  Including  books  each  one  of  which  definitely 
adds  something  new  to  the  collection.  We  aim  at  including 
representatives  of  every  variety,  every  distinct  species,  and 
thus  to  cover  the  entire  ground  in  a  way  which  shall  do 
justice  to  its  many-sidedness. 

How  Far  Realisable?  (A)  With  Mind-Made  Entities.— In 
grouping  objects  together  so  as  to  form  classes,  how  far  can 
we  realise  this  aim  of  objectivity  and  completeness?  Let  us 
consider  first  the  case  of  mind-made  entitles,  ^an  we  form 
a  class  of  musical  instruments  in  a  way  that  shall  be  objec- 
tive and  complete?  Let  us  see.  We  take  first  of  all  instru- 
ments which  produce  musical  tones  by  means  of  striking  a 
vibrating  cord — such  as  the  monocord,  clavlcord,  clavecin, 
piano,  etc.,  then  Instruments  which  produce  musical  tones  by 
means  of  pulling  or  plucking  a  cord — such  as  the  harp,  guitar, 
the  whole  lyre  family,  the  spinet,  etc.,  then  instruments  which 
produce  the  sound  from  cords  by  bowing— as  the  violin  and 
the  whole  viol  family — then  the  group  of  percussion-instru- 
ments— such  as  the  drum — woodwind  instruments — such  as 
the  flute  family — reed  Instruments — such  as  the  oboe,  clar- 
inet, etc.,  on  the  one  hand,  and  the  harmonium  on  the  other, 


310 


CLASSIFICATION 


+ 

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V 

1 

e<c.,  etc.  In  short,  by  classing  instruments  together  in  groups 
according  to  the  way  in  which  the  tones  are  produced 
we  could  try  to  find  a  place  for  everything.  Such  a  class 
would  certainly  be  objective — for  It  would  really  group 
together  actual  types  of  musical  instrument — and  there  is  also 
no  doubt  that  it  can  be  reasonably  complete.  Indeed,  so  far 
back  as  we  have  historical  records,  it  can  be  entirely  com- 
plete. 

Let  us  take  another  Instance.  Can  we  construct  a  class 
of  curved  lines  which  shall  be  both  objective  and  complete? 
Let  us  see.  A  curve  is  anything  from  a  circle  on  the  one 
hand  to  almost  a  straight  line  on  the  other.  We  can  put 
together  a  class  of  regular  curves,  composed  of  representa- 
tives of  the  circle-group — the  circumference  of  a  larger  circle 
is  less  curved  than  the  circumference  of  a  smaller  circle,  and 
the  arc  of  a  circle  of  infinite  radius  would  be  a  straight  line 
— of  the  ellipse-group,  of  the  parabola-group,  etc.,  and  thus 
secure  a  class  which  is  certainly  objective,  and  is  reasonably 
complete — in  fact,  entirely  complete.  For  although  the  num- 
ber of  possible  degrees  of  curvature  is  theoretically  unlimited, 
the  whole  ground  has  been  covered.  So  too  with  books,  pic- 
tures, and  tools  of  any  and  every  sort.  All  mind-made  entities 
can  be  classified  in  a  way  which  is  both  objective  and  complete. 

(B)  With  Natural  Phenomena. — We  classify  natural  phe- 
nomena, not  directly,  but  through  the  medium  of  mental 
models.  For  instance,  if  faced  with  a  collection  of  articles  so 
heterogeneous  that  we  can  bring  them  under  no  other  single 
head,  we  proceed  to  make  an  "inventory"  of  them.  That  is  to 
say,  we  make  a  list  of  all  the  articles,  with  the  numbering 
1,  2,  3,  4,  .  .  . — t.  e.,  put  them  together  in  terms  of  a 
mathematical  type  of  mental  model.  This  is  not  perfectly 
exact,  from  an  objective  viewpoint.  For  on  the  inventorial 
list  every  object  listed  counts  for  one,  and  none  counts  for 
more  than  one,  and  this  standard,  when  applied  to  diverse 
objects,  is  often  a  traversty.  But  from  the  view  point  of  com- 
pleteness It  leaves  little  to  be  desired,  for  it  certainly  covers 
the  whole  field,  though  in  a  very  preliminary  way.  So  too 
in  geology  we  classify  the  various  crystals  in  nature  in  terms 
of  a  mathematical  group  consisting  of  the  tetrahedron,  octo- 
hedron,  dodecahedron,  etc.  But  the  mathematical  group 
includes  forms  not  found  in  nature,  such  as  the  eikosihedron, 
and  the  actual  forms  never  perfectly  correspond  to  the  mathe- 


TYPES  OF  CLASSIFICATION 


311 


matical  models,  so  that,  while  the  raathematical  series  is  com- 
plete— for  it  certainly  covers  the  whole  possible  field— It  is 
not  perfect  in  respect  of  objectivity.  So  too  in  chemistry  the 
various  elements,  when  arranged  In  relation  to  atomic  weight, 
are  found  to  lie  on  a  spiral  curve,  and  by  investigating  cor- 
respondencies suggested  by  this  mathematical  model,  many 
important  discoveries  have  been  made.  But  here  too,  there 
are  gaps,  and  the  spiral  is  more  perfect  than  the  empirical 
facts  which  it  puts  together  into  a  group.  That  is  to  say,  it 
is  perhaps  too  complete,  and  is  not  perfect  in  respect  of  objec- 
tivity. 

At  the  same  time  it  must  be  admitted  that  classification  of 
natural  phenomena  in  terms  of  such  mental  models  is  cer- 
tainly of  very  great  assistance  in  bringing  us  into  objective 
contact  with  the  actual  varieties  of  natural  objects,  and  that 
the  progressive  insight  into  the  objective  facts  which  is  thus 
brought  about,  could  probably  not  be  brought  about  in  any 
other  way.  Classification  of  natural  objects,  then,  progres- 
sively approximates  to  objectivity,  but  is  never  perfectly 
objective.  It  is,  however,  complete,  in  the  sense  of  covering 
the  whole  ground — that  Is  to  say,  complete  in  a  somewhat 
external  way,  as  an  inventory  may  be  complete,  whatever  the 
objects  thus  assembled,  and  whether  they  have  any  inner 
relation  to  one  another,  or  not. 

Types  of  Claulfication. — The  most  elementary  type  of  class- 
ification is  the  inventory,  a  simple  mathematical  model  with 
no  pretensions  to  going  deeply  into  the  nature  of  the  sub- 
ject studied.  Objects  are  simply  numbered,  quite  arbitrarily, 
aa  1.  2,  3,  4 in  the  order  in  which  the  classify- 
ing clerk  happens  to  come  across  them.  The  best  known 
and  perhaps  most  frequently  used  of  all  types  of  classification 
is  a  refinement  upon  this.  It  is  called  index  classification. 
This  also  is  largely  accidental  and  arbitrary,  and  does  not 
go  far  into  the  nature  of  the  subject.  But  by  confining  the 
number  of  classes  to  twenty-six  which  are  grouped  from  A  to 
Z,  a  great  step  has  been  taken  towards  introducing  order  and 
system.  Because  of  its  very  great  convenience  for  purposes 
of  reference,  this  alphabetical  model  is  used  in  classifying 
all  sorts  of  objects — e.  g.,  in  filing  away  letters  of  all  kinds,  in 
libraries,  in  commercial  offices,  in  administrative  work,  in 
research  work,  and  generally,  wherever  It  can  be  applied. 
There  are  many  variants  upon  this  principle,  and  we  have 


ii- 


J12 


CLASSIFICATION 


card-index  systems  based  upon  the  days  of  the  month,  or  of 
the  week,  or  of  the  hours  of  the  day,  or  of  a  series  of  years, 
etc.  There  is  no  absolute  limit  to  its  usefulness,  or  to  the 
variations  of  model  which  may  be  employed. 

Another  common  kind  of  classification  is  the  diagnostic 
type.  This  resembles  index  classification,  in  that  it  is  used 
largely  for  purposes  of  reference,  but  at  the  same  time  goes 
somewhat  further  into  the  nature  of  the  subject  studied.  The 
characteristics  used  for  forming  the  group  are  selected  upon 
the  basis  of  being  striking  and  immediately  evident,  and  thus 
tend  to  be  somewhat  external  and  superficial.  But  they  are 
not  so  superficial  as  the  initials  A,  B,  C,  ...  Thus  a 
physician  readily  classifies  a  disease  by  reference  to  the  most 
striking  symptoms,  and  many  an  amateur  botanist  finds  out 
to  what  family  the  specimens  he  discovers  belong,  by  looking 
them  up  in  a  book  especially  written  from  this  viewpoint.  So 
too  the  common  way  of  judging  character  on  the  basis  of 
general  appearance  and  readiness  in  conversation  belongs  to 
this  type,  and  in  fact  most  of  us  carry  around  in  our  heads 
a  ready-reference  system  of  this  general  type,  for  dealing  with 
any  subject  in  which  we  are  especially  interested. 

A  further  type  of  classification,  common  in  pure  science, 
goes  more  deeply  into  the  general  nature  of  the  subject  studied. 
Thus,  the  kind  of  classification  which  we  find  in  zoology  and 
botany  attempts  to  group  together  animals,  or  plants,  accord- 
ing to  their  family  relationships,  and  generally  to  trace  their 
descent,  according  as  the  various  genera  and  species  seem  to 
have  developed  in  nature.  Because  biologists  thus  follow 
lines  of  organisation  established  by  nature,  this  type  is  some- 
times referred  to  as  vatural  classification,  though  there  has 
been  among  logicians  an  attempt  to  extend  the  usage  of  this 
term  so  as  to  cover  all  cases  of  classification  of  a  certain  type. 
Thus  classification  tends  to  be  called  natural,  where  the  group- 
ing seems  to  deal  with  the  subject  less  from  isolated  and 
arbitrary  viewpoints  which  cut  across  all  "natural"  class-dis- 
tinctions, and  more  from  insight  into  some  law  which  seems 
fundamental  in  explaining  the  various  characteristics  of  the 
object  as  a  whole,  as  the  principle  of  evolution  helps  to 
explain  a  very  great  number  of  characteristics  in  biology  and 
anthropology.  We  must  admit,  however,  that  from  a  strictly 
logical  viewpoint  this  form  of  classification  also  is  arbitrary; 
tor  the  scientist  has  a  special  Interest  in  tracing  lines  of 


VALIDITY  OF  CLASSIFICATION 


313 


descent,  and  to  group  animals  In  terms  of  mere  family  rela- 
tionships may  be  highly  artificial.  We  see  this  especially 
when  It  comes  to  classing  together  objects  whose  structure  is 
very  different — such  as  (1)  thriving  members  of  <  group  and 
(2)  degenerate  parasites  which  are  the  suckers  h^d  hangers 
on  of  animal  society,  sana  eyes,  aans  legs,  aana  almost  every- 
thing except  their  great  thirst  and  their  family  tree. 

If,  however,  we  set  out  to  classify  the  various  typical  forms 
of  classification,  we  soon  find  that  they  are  too  numerous,  and 
based  upon  too  great  a  variety  of  interests,  to  be  fully  class- 
ified. Some  follow  structural  lines,  others  follow  functional 
lines,  and  many  of  the  special  models  employed  defy  any 
general  naming.  The  fact  is,  types  of  classification  may  be, 
and  should  be,  nearly  as  numerous  as  the  interests  and  ques- 
tionings with  which  we  approach  the  phenomena  of  experi- 
ence. These,  however,  are  too  numerous  and  too  diverse  to 
be  classified  profitably,  at  least  at  the  present  stage  of  knowl- 
edge. 

Validity  of  Classification.— Not  all  classifications  are  cor- 
rect. On  library  shelves,  books  are  generally  grouped  together 
primarily  in  respect  of  content  and  secondarily  in  respect 
of  alphabetical  considerations.  Thus,  all  encyclopedias  are 
grouped  together,  and  all  books  on  logic  are  grouped  together, 
although  within  the  group  the  books  written  by  authors  whose 
surnames  begin  with  A  are  placed  first,  etc.  It  so  happens 
that  a  well-known  work  on  logic  was  originally  published  as 
volume  1  of  a  projected  "encyclopedia  of  the  philosophical 
sciences."  The  other  volumes  have  never  appeared,  but  the 
volume  on  logic  will,  in  many  libraries,  be  sought  in  vain 
where  it  should  be — among  the  books  on  logic,  and  will  be 
found  where  it  has  no  right  to  be — between  two  of  the  ency- 
clopedias. Classifications  are  thus  sometimes  incorrect.  On 
what  does  their  validity  or  invalidity  depend?  It  depends 
solely  upon  whether  they  serve  their  special  purpose,  and 
help  us  to  understand  the  objective  nature  and  objective  con- 
nections of  the  phenomena  studied.  Thus  a  certain  group  of 
organisms  Is  classified  by  the  botanists  as  belonging  to  plant- 
life,  under  the  name  Myxomycetes,  and  by  the  zoologists  as 
belonging  to  animal-life,  under  the  name  Mycetozoa,  and  among 
primitive  organisms  many  are  grouped  in  this  two-fold  way. 
Tet  such  classifications  are  perfectly  legitimate,  for  they  cer- 
tainly help  in  understanding  the  phenomena  under  study. 


li 


314 


CLASSIFICATION 


ii 

III' 


and  tbeae  certainly  have  connections  with  plant-life  on  the 
one  hand  and  animal  life  on  the  other.  Any  method  of 
claaaincatlon,  or  any  group  of  methoda.i  Is  valid,  so  far  as  It 
brings  us  Into  objective  contact  with  the  phenomena  under 
study.  In  such  a  way  as  to  help  on  the  advance  of  science. 

Function    of    Classification    in     Exposltlen^In    sclentlflo 
exposition,  classification  and  division  exercise  two  main  func- 
tions.    In   the  first  place,  classification  has  the  preliminary 
function  of  collecting  and  arranging  the  material  as  a  prep- 
aration for  proof.    The  Importance  of  this  function  can  hardly 
be  over-estimated.       It  is  only  so  far  as  the  material  has 
been   well   organised   In   this  preliminary   way  that  we  can 
be  sure,  e.  g.,  that  our  proof  has  dealt  with  all  the  points 
which  stand  out  as  Important,  and  also  that  It  has  covered  the 
whole  ;,round.     That  is  to  say,  the  objectivity  and  complete- 
ness of  an  exposition  depend  largely  upon  the  efficiency  of 
the  preliminary  classification.     Incidentally  a  good  classifica- 
tion adds  to  the  clearness  of  our  exposition.    When  we  can 
see  that  a  subject  properly  has  three  main  divisions,  each 
of  which  has  two  sub-divlslons.  etc.,  that  of  Itself  assists  us 
In  seeing  our  way  through  the  subject.    The  first  function  of 
classification,  then,  is  the  preliminary  work  of  so  organising 
the  material  for  exposition  that  we  can  proceed  to  a  proof 
which  shall  plainly  be  objective  and  shall  patently  cover  the 
whole  ground. 

In  the  second  place,  classification  and  division  are.  as  we 
have  seen,  a  form  of  organisation  which  Is  of  a  certain  general 
type.  When  we  classify,  we  place  Individuals  In  a  class  which 
Is  Itself  part  of  an  organised  system,  and  the  Individuals 
receive  a  considerable  Increment  of  meaning  from  being 
placed  in  such  a  class.  For  Instance,  man  as  a  bare  individual, 
apart  from  his  place  In  society.  Is  a  poor  thing.  Alexander 
Selkirk  was  monarch  of  all  he  surveyed,  but  he  surveyed 
little  which  was  of  importance  to  him  as  a  man,  unless  he 
gave  It  a  distinctly  social  reference.  Place  the  Individual  In 
the  class  "member  of  a  family."  and  his  significance  at  once 
Increases  proportionately.  As  a  husband  and  father  he  Is 
more  of  a  man  than  when  monarch  of  a  desert  Island,  and 
If  we  place  him  in  the  class  "citizen"— i.  e..  In  the  class  of 
men  who  think  for  themselves  on  political  questions,  and  vote 

..J  ^-  "••  Rosannuet's  application  of  botanical  oatPgorleB  to  lojric  This 
•tranweMlon  Into  another  kind"  was  deliberately  practised  by  Boyce 
In  seminar-work  with  advanced  students.  •"-"■•eu  uy  ttoyte 


VALIDITY  OF  CLASSIFICATION 


315 


as  they  think  right,  bis  ■tgnlflcance  Increasea  still  ore.  He 
takes  his  place  in  the  forward  march  of  humanity.  When 
further  we  place  him  In  relation  to  science,  art,  and  religion, 
we  begin  to  realise  ■omething  of  his  full  stature,  and  to  form 
a  more  adequate  Idea  of  man's  place  In  nature.  That  is  to 
say,  this  second  function  of  classlflcation  consists  In  remedy- 
ing, to  some  extent,  the  one-sldedness  and  arbitrariness  of 
many  of  our  preliminary  classifications.  Final  classlflcation 
endeavors  to  take  a  large  view  of  the  subject  in  all  its  more 
fundamental  relations.  In  this  way  It  leads  gradually  to 
placing  the  subject  In  Its  full  setting.  In  Its  proper  place 
in  the  system  of  acientiflc  knowledge. 

Summary. — Classlfloatlon  la  thus  a  kind  of  organisation 
which  assists  in  the  advance  of  science.  In  exposition  it 
gives  us  clearness,  objectivity,  and  completeness,  especially 
when  we  are  dealing  with  mind-made  entities,  but  also  to  a 
considerable  extent  when  we  are  dealing  with  the  world  of 
natural  phenomena.  Its  typical  forms  are  valid  so  far  as  they 
lead  to  genuine  Insight,  and  classification  as  such  on  the 
one  hand  prepares  the  way  for  proof,  and  on  the  other  leads 
logically  to  the  construction  of  a  system  of  the  departmental 
sciences. 

FOR  FURTHER  RBADINO 

H.  Lotze.  Lofflc.  pp.  120-142.  Chr.  Slgwart.  Logic,  Vol.  II,  pp.  158- 
168.     W.  Wundt.  Loglk.  (3rd  Edit.),  Vol.  II,  pp.  47-64. 


EXERCISES 

1.  In  how  many  ways  might  the  following  be  UHcfuIly  classined  : 
Man,  month,  mountain,  river,  wind,  nation.  Island,  country,  tree, 
state,  city,  girl,  book,  frog,  bulrush,  rhododendron,  life,  consclousneaa, 
Robinson  Crusoe,  Mt.  Blanc,  Ruskin,  October,  America,  oak,  Minne- 
apolis, death,  plant  .\2,  dinner,  penknife,  prayer.  New  York,  Mary, 
animal  V 

2.  Is  there  any  viewpoint  from  which  the  following  <  lasslflcatlons 
are  strictly  legitimate:  (a)  Clothiers,  land-ladles,  book-sellers,  (bt 
Children,  barking  dogs,  automobiles.  (c)  A  candid  friend,  and  a 
deadly  enemy,  (d)  A  lama  (as  deQned  In  the  exercises  to  the  pre- 
(cdlng  chapter)  and  an  unsuccessful  literary  man.  (e)  Poetry,  paint- 
ing, music,  dancing,  (f)  Corn-stalks,  wood  ahavlngs,  and  old  news 
papers? 


CHAPTER  XXIX 


PROOF 


f 


Proof  is  considered  such  an  important  part  of  logic,  that 
certain  logicians  have  defined  logic  as  the  science  of  infer- 
ence and  proof,  and  in  the  ordinary  consciousnfiss  there  still 
lingers  on,  the  medieval  conception  of  the  logician  as  the 
trained  reasoner  "who  makes  the  schools  ring  with  his  sic 
proho."  In  modern  logic,  however,  it  is  discovery  which  is 
regarded  as  the  chief  function  of  trained  thought,  and  proof 
is  relegated  to  a  very  secondary  position.  It  is  still  regarded 
as  important,  and  part  of  the  training  of  every  scientist  con- 
sists of  proving  some  thesis,  usually  in  connection  with  the 
attainment  of  an  academic  degree.  In  exposition  it  is  vital, 
and  almost  all  the  methods  used  in  definition  and  classifica- 
tion are  employed  as  preliminary  to  the  real  work  of  exposi- 
tion— proving  one's  thesis. 

Nature  of  Proof. — We  prove  by  first  constructing  a  hypo- 
thetical mental  model  and  then  testing  it  to  see  whether  It  is 
correct,  i.  e.,  whether  it  actually  applies  in  detail  to  the  situa- 
tion In  which  we  are  interested.  In  certain  cases  the  mental 
model  is  a  re-construction  rather  than  a  construction.  Thus, 
given  a  long  addition  sum,  we  construct  a  mental  model  by 
adding  from  below  upwards,  from  the  bottom  of  each  column 
to  the  top,  in  the  ordinary  way.  But  in  order  to  prove 
whether  our  answer  is  correct  or  not,  we  re-construct  the 
situation  by  adding  again.  We  may  add  in  precisely  the  same 
way  as  before,  or  we  may  start  at  the  top  of  each  column 
and  proceed  downwards.  Another  form  of  reconstruction  «.n 
frequent  use  is  to  divide  the  whole  column  up  into  tens,  and 
add  up  each  ten  lines  separately,  then  each  ten  of  those  ten, 
and  so  on,  until  the  whole  is  added.  The  second  addition,  or 
the  addition  in  some  other  direclion,  is  a  way  of  guarding 
against  misleading  associations,  and  assuring  ourselves  that 
we  have  really  counted  all  the  figures  and  have  omitted  or 
misread  nothing. 
Let  us  examine    another    example.      Let    us    prove    that 


316 


NATURE  OF  PROOF  317 

AB=BA.  We  begin  by  constructing  a  mental  model.  Let 
.   .   .  .=A,  and  let =B.   Then =1  row  of  B. 

'.'.'.'.  '.=2  rows  of  ^,  and ^^  rows  of  B. 

We  now  proceed  to  prove  that  A  rows  ot  B  =  B  rows  of  A. 
If  we  turn  the  mental  model  which  we  have  constructed,  upon 
its  side,  we  see  that  the  top  row  makes  1  row  of  A,  that  the 
two  top  rows  make  2  rows  of  A,  and  that  the  whole  figure 
makes  B  rows  of  A.  That  is  to  say,  our  mental  model  is  at 
one  and  the  same  time,  (1)  .1  rows  of  B,  and  (2)  B  rows 
of  A,  and  we  can  realise  this  by  counting  vertically  and 
horizontally.  We  then,  by  a  reconstruction  in  which  we  use 
crosses  or  other  symbols  in  place  of  the  dots,  come  to  realise 
that  the  symbols  used,  and  also  the  actual  number  of  the 
symbols,  make  no  difference  to  the  truth  of  the  model — so 
that  AX  B  =  B  XA  generally.   Q.  E.  D. 

The  whole  point  of  the  proof  in  this  case  consists  simply 
in  our  apprehending  what  we  have  done  in  our  construction. 
We  find  that  in  constructing  A  rows  of  B,  we  were  at  the 
same  time  inevitably  constructing  B  rows  of  A.  That  is,  we 
find  that  AB  and  BA  are  two  aspects  of  a  single  construction. 
It  is  a  case  of  reason  apprehending  what  it  has  itself  put  into 
the  figure,  and  becoming  perfectly  conscious  of  the  implica- 
tions of  its  own  procedure.  This  example  may  be  regarded  as 
representative  of  all  algebraical  proofs  of  the  kind  we  use  in 
solving  problems  by  means  of  equations — let  x  =  this  and 
y  =  that,  etc. — and  indeed  as  representative  of  all  mathemat- 
ical proofs  generally.i 

Let  us  take  a  non-mathematical  case.  In  order  to  prove 
whether  black  is  or  is  not  a  positive  sensation,  we  first  con- 
struct the  appropriate  situation,  and  then  observe  whatever 
i«  to  be  observed.  The  "construction"  here  consists  in  enter- 
ing the  laboratory  dark  room  and  closing  the  door.  The  con- 
ditions being  experimentally  controlled,  we  may  be  certain 
that  no  ray  of  light  will  enter  to  stimulate  the  eye,  and  that 
accordingly  here,  if  anywhere,  the  sensation  of  black  is  to  be 
experienced.  The  "proof"  consists  simply  In  observing  closely 
our  visual  sensations,  from  the  first  confused  blur  of  after- 

.lu'^i  ?'"^"*  is  advised  to  look  up  a  few  of  the  Euclidean  proofs, 
with  their  three  stajfes,  (1)  ntatetnent  of  the  problem,  (21  construc- 
tton  of  an  appropriate  situation,  and  (3)  "proof,"  or  Insight  Into  the 
relations  tnTolved  In  the  constructed  figure.  In  order  to  verify  this 
statement. 


i\ 


318 


PROOF 


Images  which  we  find  on  first  entering  the  room,  to — what- 
ever ultimately  results.  When  we  reach  this  ultimate  state 
of  the  visual  organs — say  in  thirty  or  forty  minutes — we  per- 
form the  experiment  over  again,  and  persuade  other  persons 
to  Join  us.  We  also  try  various  other  kinds  of  construction — 
such  as  looking  at  a  piece  of  "Hering  black"  paper,  at  a  piece 
of  black  velvet,  etc.  If  the  results  agree,  we  regard  our 
answer  to  the  problem  as  proved,  much  as  in  the  case  of  the 
addition  sum  considered  above.  The  stringency  of  the  proof 
depends  largely  upon  the  appropriateness  of  the  situation  and 
the  strictness  with  which  the  conditions  are  experimentally 
controlled.  Thus  the  velvet  is  better  than  the  paper,  and  the 
dark  room  is  better  than  either,  and  hero  also,  the  whole  point 
of  the  proof  seems  to  consist  in  our  apprehendir  k  what  we 
have  ourselves  brought  about  by  means  of  the  "construction." 

Aim  of  Proof  (A)  Objectivity.— The  aim  of  proof  in  logic 
Is  always,  in  the  first  place,  objectivity.  It  is  from  the 
structure  of  the  phenomenon  under  study  that  we  try  to 
prove  that  things  must  be  so  and  not  otherwise.  A  mental 
model  which  was  not  a  model  of  the  phenomenon  under 
consideration  would  be  so  far  irrelevant,  and  worthless  as 
evidence.  We  proceed  by  constructing  the  phenomenon  itself, 
or  at  least  a  mental  model  which  is  as  objective  as  may  be, 
in  order  to  see  our  way  into  the  case  actually  before  us. 
In  proving  his  thesis,  a  scientist  always  endea«ors  so  to 
arrange  and  marshal  the  objective  evidence  as  to  make  it 
plain  to  his  colleagues  that  he  has  kept  in  closest  touch 
with  the  objective  facts  throughout,  and  that  his  construc- 
tion is  of  objective  significance.  Anything  else  would  be 
recognised  as  being  beside  the  point,  and  thus,  from  a  logical 
point  of  view,  entirely  worthless.^ 

(B)  Completeness. — In  the  second  place,  proof  aims  at 
completeness.  If  there  are  five  vital  elements  in  the  situ- 
ation, it  will  not  do  to  prove  only  two  or  even  three.  It  is 
necessary  to  prove  all  five.  For  example,  if  we  wish  to 
prove  that  Mr.  Ts  dog  bit  the  president's  dog  so  that  the 
president's  dog  died,  it  is  necessary  to  prove  (1)  that  one 
dog  did  actually  bite  another,  (2)  that  the  dog  which  did 
the  biting  was  Mr.  Z'«  dog,  and  (3)  that  the  dog  which  was 
bitten  was  the  president's  dog,  and  (4)  that  the  bitten  dog 
died,  and  (5)  died  in  consequence  of  the  bite.    In  a  case  of 

ifCf.  the  case  of  A'-rays,  referred  to  above   (p.  102). 


AIM  OF  PROOF 


319 


this  kind  which  the  writer  has  In  mind,  (3)  and  (5)  were 
never  proved,  though  there  was  "strong  presumptive  evl- 
dence."  In  actual  fact,  however,  the  president's  dog  was 
not  bitten,  and  is  still  alive. 

Our  construction  of  the  mental  model  must  include  all  the 
relevant  features.  Thus,  in  the  attempted  "proof  that  the 
universe  is  equal  in  size  to  a  lump  of  sugar,  because  each  is 
divisible  to  infinity,  and  Inflnitles  are  equal— it  is  forgotten 
that  division  in  no  way  Increases  or  diminishes  the  8ize  of 
the  object  divided,  so  that  If  the  sizes  were  strikingly  dif- 
ferent before  division,  they  will  remain  strikingly  different 
after  division,  however  much  Infinities  may  be  numerically 
equal.  The  omission  would  be  at  once  observed  if  It  had  been 
urged  that  each  object  could  be  divided  into  two  halves  or 
four  quarters,  and  that  two  halves  =  two  halves,  or  four 
quarters  =  four  quarters,  etc.  But  once  the  word  "infinity" 
is  used,  the  vital  omission  seems  to  escape  our  attention. 
Our  mental  model,  then,  must  be  not  only  objective,  but  also 
complete. 

How  Far  Realisable?  (A)  With  Mlnd-Made  Entitle*.— How 
far  can  this  aim  be  realised?  Let  us  consider  first  the  case 
of  mind-made  structures.  Mathematical  examples  have  been 
given  above,  and  mathematical  proof  Is  sometimes  taken  as 
a  type  of  what  demonstration  should  be,  strict,  rigorous, 
exact.  We  proceed  by  constructing  a  mental  model,  com- 
posed of  dots,  lines,  or  other  quantitative  or  spatial  symbols, 
and  seem  by  these  means  to  obtain  an  insight  into  the  Inter^ 
relation  of  the  parts  of  our  mental  model— an  Insight  which 
is  usually  satisfactory  in  point  of  both  obJecUvIty  and  com- 
pleteness. In  the  world  of  mathemaUcal  entitles,  where  our 
mental  model  and  the  subject  we  are  studying  coincide,  there 
can  be  no  doubt  of  the  objective  reference  of  our  pro- 
cedure. We  construct  the  object  Itself,  and  in  so  doing  come 
to  realise  its  various  Implications.  In  a  way  which  we  find 
adequate,  though  not,  perhaps,  Incapable  of  Improvement. 

In  respect  of  completeness,  however,  a  certain  doubt  may 
be  felt.  It  is  well  known  that  the  proofs  of  many  of  the 
theorems  in  Bk.  Ill  of  Euclid  employ  the  full  definition  of 
the  circle,  in  cases  where  a  knowledge  of  conic  sections 
shows  that  something  less  than  the  full  ■  definiUon  of  the 
circle  would  have  been  sufficient.  That  is  to  say,  certain  of 
these  proof-models  are  too  complete,  in  that  they  use  too 


lij' 


320 


PROOF 


if: 


much  argument  and  evidence,  Including  certain  elements 
which,  strictly  taken,  are  irrelevant.  Further,  the  existence 
of  "alternative"  proofs  raises  a  certain  doubt.  Are  such 
proofs  equally  objective,  and  equally  complete?  Compare, 
e.  g.,  the  modern  proof  of  Euclid  1.  13  with  the  original  proof. 
The  modern  proof  takes  a  straight  line  ABC,  and  points  out 


Ui\ 


A  B  "C 

that  the  angle  ABC  =  two  right  angles.  By  taking  a  straight 
line  BD,  pivoting  on  B,  and  moving  from  a  position  coinciding 
with  BA  to  a  position  coinciding  with  BC,  It  is  easily  realised 
that  the  space  ABC  remains  equal  to  two  right  angles,  how- 
ever it  may  be  divided  up  by  the  successive  positions  of  BD. 
This  is  far  more  direct  than  the  Euclidean  proof,  which  makes 
use  of  the  addition  of  equals  to  equals,  etc.,  and  does  not  give 
so  much  insight  into  the  spatial  relation  involved  as  is  given 
in  the  modem  proof.  The  proof  which  is  more  direct  appears 
to  be  more  objective  and  more  complete. 

Let  us  take  another  example.  How  do  we  prove  that  "The 
supply  of  game  for  London  is  steadily  going  up  .  .  ." 
means  "The  game  is  up  .  .  ."?  We  prove  it  by  con- 
structing the  plan  of  the  cipher — every  third  word — and  then 
reading  off  the  first,  fourth,  seventh,  etc.,  words,  and  finding 
that  these  make  sense,  and  a  sense  which  is  strictly  appro- 
priate to  the  whole  situation.  The  proof  consists  in  con- 
structing a  mental  model  which  really  gives  insight  into  the 
relations  involved,  and  is  in  fact  the  model  in  accordance 
with  which  the  cipher  was  originally  constructed.  The  clinch- 
ing element  about  the  proof  is  that  it  works.  Its  details 
coincide  with  the  details  of  the  example,  just  as  in  Ehiclid's 
superposition  method  the  triangle  ABC  coincides  with  the 
triangle  DEF,  and  it  makes  sense,  i.  e.,  perfectly  fits  the  cir- 
circumstances.  Such  a  proof  is  both  objective  and  complete,  for 
the  mental  model  exactly  coincides  with  the  object  in  ques- 
tion. In  geometry,  however,  where  we  are  stud>ing  the  nature 
of  space,  and  this  is  not  entirely  mind-made  even  though 
we  move  in  an  almost  closed  circle  of  definitions,  postulates, 
and  axioms, — i.  e.,    mental    models — our    proof   was   not   so 


AIM  OF  PROOF 


121 


wholly  obJecUve  and  complete.  In  dealing,  then,  with  mind- 
made  entities,  we  can  say  that,  so  far  as  they  are  truly 
mind-made,  our  proofs  can  be  both  objective  and  complete, 
but  that  so  far  as  they  are  not  fully  mind-made,  but  deal 
with  such  an  entity  as  the  nature  of  space,  they  are  not  fully 
objective  and  not  fully  complete,  but  admit  of  scientific  prog- 
ress in  both  these  directions. 

(B)  With  Natural  Phenomena.— In  dealing  with  objects 
other  than  mind-made  entities,  we  use.  as  we  have  already 
seen,  mental  models  for  most  of  our  intellectual  operations. 
Proof  is  no  exception  is  this  general  rule,  and  proof  moves 
wholly  within  the  realm  of  mental  models,  especially  of  a 
mathematical  type.  We  realise  this  especially  In  the  case  of 
physical  science.  Such  proofs  deal  with  objects  only  in 
respect  of  their  mathematical  properties — *.  c,  only  so  far  as 
they  coincide  with  ideal  units,  ideally  straight  lines,  etc. 
Thus  we  prove  that  if  a  ladder  slides  down  a  wall,  the  path 
described  by  someone  who  is  in  the  middle  of  the  ladder  will 
be  the  arc  of  a  circle.  But  this  is  strictly  true  only  if  we 
suppose  the  ladder  to  be  fairly  represented  by  a  mathe- 
matically straight  line,  the  side  of  the  house  and  the  surface 
of  the  ground  by  a  mathematically  exact  right  angle,  and  the 
person  in  question  to  be  occupying  the  mathematical  center 
of  the  ladder.  It  is  well  known  that-  a  certain  allowance  has 
to  be  made,  in  practise,  for  some  divergence  from  the  exacti- 
tude of  the  mathematical  model,  and  that  such  proofis  are 
thus  not  entirely  objective  and  not  entirely  complete. 

Let  us  take  another  example.  In  laboratory  psychology 
there  is  an  experiment  with  free  associations  which  bears 
upon  criminology.  A  student  commits  one  of  two  artificial 
"crimes,"  the  conditions  of  which  are  established  beforehand 
by  the  experimenter.  The  experimenter  does  not  know  which 
of  the  two  he  has  committed,  but  proceeds  to  test  him  by 
calling  for  associations  in  connection  with  a  list  of  stimulus- 
words,  some  of  which  bear  upon  crime  A,  and  some  on  crime 
B.  The  reaction-time  for  each  association  is  taken,  and  if 
the  reaction-time  for  associations  connected  with  crime  A  li 
noticeably  longer,  on  the  average,  than  the  reaction-time  for 
associations  connected  with  crime  B,  the  student  Is  pro- 
nounced guilty  of  crime  A.  The  proof  consists  in  construct- 
ing the  two  possible  association-situations,  and  seeing  whidi 
gives  the  longer  reaction-time.    There  is  an  average  reaction- 


522 


PROOF 


time  for  every  individual,  and  a  noticeable  departure  from 
that  reaction-time  must  have  a  special  reason.  For  laboratory 
purposes,  such  a  proof  is  regarded  as  sufficients 

In  actual  laboratory  practise,  this  mental  model  works 
fairly  well,  and  in  medical  practise  Psycho-analysts  use  It 
as  a  regular  method  of  Investigation.  But  It  is  neither  per- 
fectly objective  nor  perfectly  complete.  There  are  nearly 
always  lengthened  reaction-times  on  the  side  of  the  crime 
which  has  not  been  committed — though  these  are  not,  as  a 
rule,  numerous— and  the  reactions  to  words  of  criminal  Import 
are  not  always  lengthy,  but  may  be  within  the  limits  of 
probable  error.  There  is  thus  room  for  Improvement  in 
the  technique  of  the  method,  and  in  general  we  may  say  that 
wherever,  as  in  the  case  of  such  natural  phenomena,  there  is 
a  gap  between  the  mental  model  which  we  employ  and  the 
facts  which  we  are  attempting  to  study  by  Its  means,  our 
proof  falls  short,  precisely  to  that  extent  and  for  that  reason, 
of  objectivity  and  completeness. 

Validity  of  Proof.— In  the  ordinary  use  of  terminology,  an 
argument  or  mental  model  must  be  valid,  before  it  is  digni- 
fied by  the  name  of  "proof."  If  it  is  not  vaUd,  If  it  faUs 
short  of  proof,  it  is  given  some  other  name,  such  as  "pre- 
sumptive evidence."  We  shall  accept  this  terminology,  and 
shall  refuse  to  regard  as  proofs,  mental  models  which  are 
invalid.  All  proofs,  then,  as  such  are  valid.  But,  as  we 
have  seen,  there  are  degrees  of  validity.  The  history  of  a 
science  such  as  mathematics  sufficiently  shows  that  a  number 
of  alternative  proofs  of  a  conclusion  are  equally  possible, 
but  that  some  of  them  enter  more  directly  Into  the  nature 
of  the  relations  studied — i.  e.,  are,  as  we  have  seen,  more 
objective  and  more  complete  than  others.  Validity  is  thus 
seen  to  be  a  matter  of  objectivity  and  completeness,  and  the 
degree  to  which  a  proof  is  valid  can  thus  be  Judged  ade- 
quately only  In  the  light  of  further  progress  In  scientific 
knowledge.  Evidence  may  be  sufficient  to  prove  our  point 
without  exhausting  the  possibilities  of  proof.  For  example, 
circumstantial  evidence  is  often  sufficient  to  prove  a  man 
guilty  in  the  courts.  But  few  authorities  would  regard  cir- 
cumstantial evidence  as  the  most  satisfactory  form  of  proof. 

•  The   method   Is  sketched  very  briefly.     For  further   Information 
consult  A.  A.  Brill.  Psvchoanaiygis.  Ernest  Jones,  PsychoanaluaU    and 
tl»e  Pap«f8  by  Jung  and  Freud  In  the  Ameriam  Journal  of  Psychology 


\\v 


TYPES  OF  PROOF 


323 


It  is  a  little  Indirect  and  external,  and  evidence  of  this  Und, 
which  looked  like  overwhelming  proof,  has  occasionally  been 
overthrown  by  evidence  of  a  more  direct  character.  Proof, 
then,  is  valid  so  far  as  it  gives  genuine  insight  Into  the 
relations  in  question,  i.  e.,  so  far  as  our  mental  model  coin- 
cides in  its  main  outlines  with  the  structure  of  the  object 
with  which  we  are  dealing.  Except  in  the  case  of  purely 
mind-made  entities  such  as  ciphers,  it  is  never  final,  but  is 
progressive,  and  the  degree  of  its  validity  can  only  be  Judged 
In  the  light  of  further  scientific  advance. 

Types  of  Proof.— The  most  frequent  model  used  for  pur^ 
poses  of  proof  is  undoubtedly  the  mathematical  type  of 
model.  In  physical  science  the  Importance  of  such  a  type 
of  proof  has  long,  been  recognised  as  supreme,  and  since 
the  days  of  Plato  the  mathematical  model  has  been  regarded 
as  constituting  almost  the  ideal  kind  of  proof.  But  taken 
strictly,  there  are  at  least  as  many  possible  types  of  proof 
as  there  are  possible  subjects  of  exposition,  and  for  some 
of  these  the  mathematical  type  of  proof  would  be  regarded 
as  merely  preliminary,  while  for  others  it  would  be  wholly 
inadequate.  For  example,  in  ethical  and  religious  questions, 
a  mathematical  type  of  proof  may  well  be  used  In  marshaling 
evidence  and  arranging  one's  data,  but  such  a  method  la 
merely  preliminary.*  It  Is  of  assistance  In  preparing  the 
ground,  but  in  dealing  with  an  ethical  question,  what  we 
desire  is  an  insight  which  Is  ethical.  So  too  In  dealing  with 
historical  questions,  or  questions  of  musical  technique,  math- 
ematical types  of  proof  can  at  best  play  only  a  very  sub- 
ordinate part.  On  the  whole,  then,  there  are  so  many  types 
of  model  which  can  be  regarded  as  possible,  that  it  is 
unprofitable  to  attempt  to  enumerate  and  classify  them. 

It  Is  usual,  however,  to  distinguish  two  typical  forms  of 
proof  which  dlfTer,  not  in  respect  of  the  kind  of  model  used, 
but  rather  In  the  way  In  which  this  Is  applied  and  In  the 
kind  of  Insight  to  which  It  leads.  These  are  known  as  (1) 
direct  proof  and  (2)  Indirect  proof.  All  the  instances  pre- 
viously studied  in  the  chapter  would  be  considered  cases 
of  direct  proof.  Direct  proof  attempts  to  construct  such  a 
mental  model  of  the  situation  with  which  we  are  dealing, 

*Fm  the  scleatlflc  application  of  mathematical  modela  to  relMoua 
quMttons,  conault  the  Journal  of  Religiout  Psychotooy,  and  cm  ethical 
questions,  the  International  Journal  of  Ethics  wi'.  "  "  ""  eiuicai 


324 


PROOF 


tbat  It  shall  be  possible  to  attain  to  a  simple,  straight^ 
forward,  and  direct  insight  into  the  relations  involved,  as 
when  we  superimpose  one  triangle  directly  upon  another,  or 
when  we  reconstruct  a  situation  which  is  in  question,  by 
appealing  to  the  evidence  of  trust-worthy  eye-witnesses. 
Indirect  proof  is  like  the  reductio  ad  ahaurdum  in  Euclid. 
It  attempts  to  prove  that  A  must  be  B  on  the  ground  that 
the  contradictory  supposition  leads  to  absurdities. 

Let  us  consider  an  example  of  indirect  proof.  To  prove 
that  A  did  not  personally  murder  B,  in  spite  of  his  known 
motive  to  do  so,  and  in  spite  of  circumstantial  evidence 
against  him,  it  Is  enough  to  prove  that  A  was  in  another 
town  at  the  exact  tim  when  the  murder  was  committed.  The 
alibi  is  a  convincing  form  of  indirect  proof.  We  construct 
a  mental  model  of  the  situation,  and  find  that  it  cannot  pos- 
sibly be  made  to  square  with  the  supposition  of  A's  personal 
guilt.  That  is  to  say,  from  direct  insight  into  the  require- 
ments of  the  situation  we  see  that  another  suggested  mental 
model  will  not  fit.  Into  this  incompatibility  also  we  have  an 
insight  which  is  direct.  An  indirect  proof  of  any  statement 
thus  consists  of  a  direct  refutation  of  the  contradictory  oppo- 
site. Hence  it  has  been  suggested  by  Herbert  Spencer  that 
a  criterion  of  truth  is  the  inconceivability  of  the  opposite, 
and  in  practise  there  is  no  doubt  that  indirect  proofs  may 
be  of  great  assistance  in  bolstering  up  an  attempt  at  direct 
proof  which  is  not  perfectly  convincing.  But  what  is  con- 
vincing about  the  so-called  "indirect"  proof,  is  not  its  indi- 
rectness, but  its  direct  side.  We  believe  that  A  could  not 
possibly  have  personally  murdered  B,  because,  we  have  direct 
proof  tbat  he  was  in  another  town,  and  because  we  can  see 
directly  tbat  it  was  necessary  for  him  to  have  been  at  the 
scene  of  the  murder  if  he  is  to  be  regarded  as  guilty  of  the 
charge.  We  compare  these  two  mental  models,  and  see 
directly  that  they  are  incompatible.  The  nature  of  proof, 
then,  is  fundamentally  to  be  direct,  and  so  far  as  It  falls 
short  of  directness,  so  far  it  falls  short  of  convincing  us  of 
Its  validity.    Logically,  then,  proof  is  always  direct. 

Summary. — ^We  prove  by  constructing  a  mental  model  of 
the  situation  in  question.  In  such  a  way  as  to  make  clear 
the  inter-relation  of  elements  in  the  model  which  we  have 
constructed.  Reflection  upon  our  own  construction  leads  to 
an  insight  which  is  direct  and  convincing.    The  aim  of  such 


VALIDITY  OF  PROOF 


S2S 


mental  models  is  objectivity  and  completeness,  and  in  oases 
where  our  construction  gives  us  the  object  itself,  this  aim 
can  be  attained.  In  the  case  of  natural  phenomena,  however, 
where  there  is  a  gap  between  the  mental  model  and  the 
phenomenon  in  question,  we  can  only  approximate  to  com- 
plete objectivity.  While  it  is  usual  to  distinguish  an  "indirect" 
form  of  proof,  the  nature  of  proof  is  essentially  direct,  and 
the  degree  of  its  validity  can  be  determined  only  in  the 
light  of  further  advance  in  knowledge.  As  knowledge  is 
never  complete,  but  progressive,  so  proof  is  never  absolutely 
final,  but  advances  with  advancing  science. 

FOR  FURTHER  READING 

H.  Lotze,  Logic,  Bk.  II,  chapter  iy.     Chr.  Slgwart,  Logic,  Vol.  II, 
pp.  192-210.    W.  Wundt,  Logik,  (Srd  Edit.),  Vol.  II,  pp.  65-85. 


EXERCISES 

How  could  you  prove:  (a)  That  you  really  are  where  yon  think 
you  are.  (b)  That  Napoleon  ever  lived,  (c)  Tnat  459  —  387  =  72. 
(d)  That  a  bird  In  the  hand  i«  worth  two  In  the  bush,  (e)  That  a 
university  dejrree  Is  a  desirable  asset,  (f)  That  Beethoven  was  one 
of  the  greatest  musicians  who  lived  within  the  last  two  hundred 
years,  {g)  That  lying  and  stealing  are  wrong,  (h)  That  life  Is 
worth  living.  (1)  That  com  will  not  grow  if  planted  early  in  the 
spring? 


CHAPTER  XXX 


FALLACIES 


'( 


Fallacies  are  older  than  logic.     Indeed,  one  of  the  chief 
motives  which  first  led  to  logical  study  was  the  reaction  from 
•ophistry  or  the  deliberate  use  of  fallacies  to  deceive  and 
entangle    others.     In    consequence   of    this    interconnecUon 
between  the  search  after  truth  and  the  avoidance  of  falsity, 
some  study  of  the  nature  of  fal  dcy  has  always  formed  an 
integral  part  of  scientific  method.    No  one  entirely  escapes 
falling  Into  these  errors.     Even  logicians  of  the  caliber  of 
John  Stuart  Mill  have  made  mistakes  In  this  way  which  othen 
have  pointed   out,  but  which  they  themselves  were  never 
able  to  see.    At  the  present  day,  fallacious  agruments  are  not 
so  frequently  used  with  deliberate  Intent  to  deceive  as  was 
perhaps  the  case  In  ancient  Athens,  and  It  is  more  a  question 
of  putting  ourselves  upon  our  guard,  so  as  not  to  fall  Into 
these  traps  which  await  each  one  of  us,  and  so  deceive  our- 
selves. 

Definition  of  Fallacy.— Fallacies  are  sometimes  defined  as 
failures  to  prove— i.  e.,  as  though  It  Is  In  relation  to  attempts 
at  proof  that  they  are  especially  noticeable.    It  Is  certainly 
true  that  a  fallacy  proves  nothing,  and  that  If  the  aim  of 
the  thinker  who  fell  Into  the  fallacy  was  to  prove  something 
he  has  failed  of  his  aim.     But  this  definition  is  not  wide 
enough  for  scientific  accuracy.    Many  a  fallacy  Into  which  we 
frequently  fall  can  hardly  be  brought  under  the  head  of  proof. 
For  Instance,   there  may   be   failures   to  judge  or  to  Infer 
correctly,  failures  in  analysis  and  synthesis.  In  abstraction 
and  determination,  failures  in  Induction  and  deduction.    And 
though  all  of  these  may  indeed  be  used  as  methods  of  proof 
they  are  far  more  frequently  used  as  methods   of  Investl- 
gaUon.     It  Is  thus  possible  to  fall  into  fallacies  In  respect 
of  Investigation,  as  well  as  In  exposIUon.    So  too  in  exposition 
there  are  fallacious  attempts  at  definition  and  classification 
as  well  as  at  proof.    There  Is  no  limit  to  the  opportunities 
for  error,  and  they  are  quite  certainly  not  restricted  to  the 


J26 


/ 


OCCASIONS  OF  FALLACY 


527 


field  of  attempted  proof.  We  shall  therefore  define  fallaoiei  ) 
as  mi$take$  in  thinking — uaing  the  term  thinking  in  ita  widest  i 
possible  sense. 

Occasions  of  Fallacy. — The  pursuit  of  truth  takes  place,  as 
we  have  seen,  by  the  construction  of  mental  models.  FUla- 
cies  arise  when  these  mental  models  are  used  in  some  way 
which  ia  incorrect.  There  are  three  main  possibilities  of  such 
incorrect  use: — (1)  in  relation  to  the  data  which  furnish  our 
starting-point — the  mental  model  which  we  construct  may 
misrepresent  the  concrete  situation  which  we  are  attempting 
to  understand,  as  when  the  paranoiac  Interprets  the  most 
innocent  actions  of  the  persons  around  him  as  the  deliberate 
designs  of  conspirators.  (2)  In  the  second  place,  there  may 
be  no  mistake  about  the  data  as  such,  or  about  their  relation 
to  the  mental  model,  but  the  model  itself  may  contain  some 
logical  flaw,  such  as  an  inconsistency.  This  is  frequently  the 
case  with  our  typical  rules  in  ethics  and  esthetics.  Unless 
formed  with  the  utmost  care,  these  rules  ottea  contain  certain 
inconsistencies  which  only  become  apparent  in  the  course  of 
time,  as  their  consequences  develop  and  lead,  perhaps,  to 
results  the  opposite  of  what  we  had  intended.!  (3)  In  the 
third  place,  the  application  of  our  mental  model  to  concrete 
facts  may  be  careless  and  so  lead  to  mistakes,  as  when  we 
attempt  to  apply  any  system  of  theoretical  principles  in 
practise,  or  to  carry  out  general  orders  in  detail.  The  appli- 
cation of  any  general  principle  is  full  of  dangers  of  this  tjrpe. 

Fallacies  of  this  general  kind  may  arise  dther  in  investi- 
gation or  in  exposition.  In  exposition,  however,  there  is  an 
additional  occasion  of  error.  This  arises  from  the  fact  that 
in  exposition  there  are  at  least  two  parties,  the  writer  or 
speaker  on  .the  one  hand,  and  the  reader  or  hearer  on  the 
other.  There  is  thus  a  certain  duality  of  outlook  which  leads, 
perhaps  inevitably,  to  certain  mistakes  in  understanding.  The 
speaker  has  his  set  of  mental  models,  and  the  hearer  has  hia. 
These  two  sets  are  bound  to  be  partly  different,  in  view  of 
the  differences  in  education  and  in  habit  of  mind.  The  hearer 
translates  what  he  hears,  into  his  own  set  of  mental  models, 
and  in  so  doing  can  hardly  escape  a  large  number  of  errors. 
We  see  this  most  clearly,  perhaps,  in  the  case  of  foreigners. 


1  For  a  number  of  instances  of  rules  taken  even  from  physical 
science,  cf.  F.  H.  Bradley,  Appearance  and  ReaUttf,  the  first  half  of 
the  hook. 


328 


FALLACIES 


hi 


11  r 


When  we  hear  an  address  Id  French  or  Qerman,  we  translate 
It  Into  our  own  ideas  or  mental  models,  and  there  is,  as  we 
all  know,  much  which  cannot  poasibly  be  translated  with 
absolute  correctness.  And  if,  perhaps,  we  do  not  understand 
French  or  German  correctly,  and  the  foreigner  in  question 
can  not  understand  u«  correctly  either,  our  attempts  at  con- 
versation are  pitiable  indeed. 

Such  fallacies  arise  from  a  difference  of  mental  model. 
What  A  means  in  one  sense,  B  may  translate  iato  an  entirely 
differMit  set  of  mental  models.  This  can  take  place  in  a 
single  language  just  as  well  as  in  two,  as  will  be  seen  if 
we  consider  one  or  two  instances. 

Where  do  you  live.  Pat?    With  Mike. 

Where  does  Mike  live?    With  me. 

But  where  do  you  and  Pat  both  11  vj?  Sure,  isn't  it  together 
that  I'm  telling  you  we  live? 

The  difficulty  arises  here  from  perfectly  honest  misunder- 
standing. The  mental  model  of  the  questioner  is  spatial.  He 
wishes  to  kno>v  Pat's  street  address,  whereas  Pat's  mental 
model  is  social,  and  has  not  the  remotest  glimmering  of  a 
connection  with  spatial  questions.  Such  mistakes  are  ex- 
tremely common  in  every  walk  of  life,  as  well  as  in  scientific 
exposition.    We  may.  perhaps,  notice  one  more  example. 

She:    Do  you  admire  me  for  my  intellect,  or  for  my  beauty? 

He:    Not  for  your  intellect. 

She:    Flatterer! 

In  this  case  She  assumes  as  an  explanation  of  their  situa- 
tion the  mental  model  of  admirer  and  admired,  while  He 
assumes  the  mental  model  of  borer  and  bored.  In  this  case 
the  divergence  of  mental  models  is  very  thinly  disguised,  and 
may  well  be  deliberate  on  both  sides,  as  is  so  frequently  the 
case  on  occasions  which  call  for  the  employment  of  social 
"tact." 

Such  cases  of  a  confusion  of  two  logically  distinct  mental 
models  may  even  happen  to  a  single  individual.  The  best 
known  Instance  is  MiU's  famous  fallacy: — 

The  only  proof  that  an  object  is  visible  is  that 
people  actually  see  it.  The  only  proof  that  a  sound  , 
Is  audible  is  that  people  actually  hear  it  And  so  of 
the  other  sources  of  our  experience.  In  like  manner, 
the  sole  evidence  that  anything  is  desirable,  is  that 
people  actually  desire  it.    People  do  actually  desire 


OCCASIONS  OF  FALLACY 


329 


PiMSure.  Therefore,  Pleasure  is  deetrable.  or  Oood, 
Ofuf  in  fact  the  Chief  Oood. 
The  anpjmeot  proves  that  pleastire  Is  something  which 
people  cmx  desire,  but  Mill  takes  it  as  proving  that  it  Is  a 
"good"  01  Bomething  which  they  ought  to  desire.  The  con- 
fusion u  thus  betwe«n  a  psychological  and  an  ethical  mental 
mod<»l  Such  mlHtalces  are  very  common  In  attempts  to  prove 
ethical,  esthelical.  or  religioUH  brtiefs  in  tenns  of  models 
which  are  psychological,  economic,  or  biological — *.  e.,  other 
than  ethical,  esthetlcal,  or  rellgiouB.^ 

Yet  another  occasion  of  fallacious  thinking  arises  from 
the  way  in  which  the  written  or  spoken  language  may  suffer 
from  Blips  m  the  mechanism  of  expression,  so  that  one  model 
is  Intended,  but  another  suggested.  This  is  extremely 
common.    E.  g.,  from  a  New  York  paper: 

WANTED.    A  groom  to  look  after  two  horses  of  a 
pious  turn  of  mind. 

A  second-hand  morris  chair  for  a  bach- 
elor with  richly  carved  claw-feet. 
In  everyday  cases  like  these,  we  can  usually  distinguish 
what  was  Intended  from  what  Is  suggested.  But  any  student 
who  has  done  much  translation  from  one  language  into 
another  will  know  that  there  are  many  ambiguities,  arising 
probably  from  some  slip  in  the  mechanism  o£  expression, 
wt»re  no  Ingenuity  can  succeed  In  discovering  what  the 
original  author  may  have  meant.  This  Is  particularly  well 
known  in  the  case  of  the  Greek  and  Latin  classics,  where  a 
most  ^aborate  technique  has  been  developed  for  dealing 
with  Just  such  errors.  In  many  cases,  however,  the  text 
proves  to  be  hopelessly  corrupt,  and  the  modem  editor  resorts 
to  emendations  of  his  own — i.  e.,  reconstructs  the  passage  In 
accordance  with  a  mental  model  which  appears  to  him  to 
satisfy  the  requirements  of  the  situation.  The  fallaciousness 
of  such  emendations,  however,  is  universally  admitted. 

From  these  considerations,  we  realise  that  the  occasions  of 
fallacies  are  to  be  sought  in  the  relation  of  our  mental 
models  to  the  facts  of  experience.  Our  constructions  may 
differ  from  the  facta  with  which  we  start,  or  from  the  facts 
to  which  we  wish  to  apply  them,  or  from  other  possible 
models  based  upon  the  same  data. 

«Cf.  Locke's  "proof"  that  It  Is  Impoaslble  to  be  a  slncer*  Atbelit, 
In  the  Buay.  Bk.  IV,  chapter  x. 


330 


FALLACIES 


n. 


Characteristic*  of  Fallacy  (A)  Subjectivity.— However  fal- 
lacies may  arise,  there  are,  however,  certain  characteristics 
which  they  one  and  all  exhibit  In  the  first  place,  fallacy  is 
subjective.  All  thought  and  all  reasoning,  whether  for  pur- 
poses of  investigation  or  for  purposes  of  exposition,  ostensibly 
aims  at  truth—  at  bringing  us  Into  connection  with  objective 
facts  and  objective  laws.  It  is  because  a  thought  somehow 
fails  of  establishing  this  connecti<Hi  that  it  is  called  a  fallacy. 
We  are  left  on  the  hither  side  of  the  fence,  and  take  our 
own  ideas,  our  mental  models,  for  the  realities.3  At  times, 
we  even  take  the  symbolic  ezoression,  the  word  itself,  for  the 
reality,  and  try  to  substitute  for  insight  into  the  reality  a 
futile  discussion  based  upon  the  philological  characteristics 
of  the  word.  Thus  a  student,  asked  in  an  examination  in 
formal  logic  to  define  the  technical  term  "contrapositive," — 
which  is  one  of  the  forms  of  "immediate  inference" — answered 
that  It  was  something  which  was  (1)  not  positive,  for  it 
was  opposed  to  the  positive  (contra  in  Latin  means  "against"), 
bui  also  (2)  not  entirely  negative.  For  example,  "counter- 
felt  money"  was  opposed  to  the  positive,  for  it  was  false 
currency,  but  was  also  not  entirely  negative,  for  you  could, 
perhaps,  succeed  in  passing  it! 

As  a  general  rule,  then,  we  fall  into  fallacies,  when  this 
takes  place,  by  getting  lost  in  the  mechanism  of  our  own 
thinking,  whether  this  is  due  to  the  complication  of  our 
mental  models,  or  arises  from  substituting  the  word  for  the 
thing.  The  mental  model  comes  between  us  and  the  reality, 
and  our  thought  remains  satisfied  with  a  superficial  inter- 
pretation, which  seems  good  to  u«,  at  least  for  the  time 
being,  but  will  not  withstand  a  serious  comparison  with  the 
objective  facts.  Thus  the  hasty  classical  student  translates 
the  famous  line  Frigidut  in  pratis  cantando  rumpitur  anguia 
as  "The  cold  meadow-snake  bursts  into  song,"  (instead  of 
"is  torn  asunder  by  magic  charms"),  or.  .  .  .  et  odora 
canum  vis  as  "and  a  powerful  smell  of  dogs,"  (instead  of  "and 
a  keen-scented  pack  of  hounds"), — and  is  thoroughly  satisfied 
with  his  entirely  original  rendering.  So  too  many  novelists 
are  satisfied  that  they  are  thoroughly  in  touch  with  real  life, 
when  as  a  matter  of  fact  they  are  revelling  in  a  world  of 
mental  models  which  are  mental  fictions.     Subjectivity,  then. 


•  <^M   In  this  connection,  the  first  few  pagea  of  Ptato'a  Republio, 


SCOPE  OF  FALLAQES 


331 


or  failure  to  get  into  touch  with  objective  fiicts,  is  one  of  the 
chief  characteriaticB  of  fallacious  thou^t 

(B)  ineompletenes*. — A  second  characteristic  of  fallacious 
thinking,  is  its  incompleteness.  We  leap  at  c(mclasions  which 
are  false,  only  because  we  do  not  pay  sufBclent  attentimi  to 
the  evidence  before  us.  If  we  always  adhered  to  careful 
methods  of  analysis  and  synthesis,  mistakes  would  man 
rarely  arise.  But  we  pass  over  something  without  noticing 
it,  and  the  consequences  of  such  a  slip,  slight  perhaps  in 
Itself,  may  be  serious.  Thus,  to  suppose  that  the  country  is 
prosperous  because  many  business  mm  are  making  money, 
and  all  our  acquaintances  happen  to  be  doing  well,  is  a 
mistake  which  arises  from  incomplete  observation.  Other 
cases  are  not  so  serious.  When  the  Home  Guard  Private 
asked,  "If  we  Join  the  National  Guards,  what  will  be  our 
relations  with  the  other  units,"?  it  was  sufficiently  obvious 
that  he  meant,  would  his  battalion — the  parent  organisation 
— be  numbered  1  or  13.  It  was  perhaps  deliberate  incom- 
pleteness of  observation  which  made  the  Major  (who  didn't 
know)  answer,  "Friec  "—at  least  I  hope  so."  So  too  with 
the  child's  reasoning,  xi  penny  is  a  ct^per  (coin),  and  a 
"copper"  is  a  p(rilceman,  and  a  policeman  is  an  officer  (of 
the  law),  and  an  officer  (of  the  naval  or  military  forces)  Is 
a  gentleman;  therefore  a  penny  is  a  gentleman."  Each  step 
in  c(mtinuing  such  an  argument  can  be  taken  only  by  one 
who  is  wilfully  blind  to  many  elements  in  each  transition. 
Incompleteness,  then,  is  a  second  characteristic  of  fallacious 
thinking. 

Scope  of  Fallacies. — There  is  no  limit  to  the  sc(9e  of  fal- 
lacious thought  In  the  sphere  of  mind-made  entities,  mis- 
takes creep  in  almost  as  readily  as  when  we  are  dealing  with 
natural  phenomena.  By  a  slight  mis-drawing  of  the  figure, 
which  passed  unobserved,  it  has  seemed  possible  to  demon- 
strate that  one  right  angle  is  equal  to,  and  greater  than, 
another  right  angle,  or  that  parallel  straight  lines  meet 
before  reaching  infinity.  So  too  in  ethical,  esth^cal,  and 
religious  thought,  the  confusion  of  mind  in  whicdi  we  so 
easily  involve  ourselves  is  too  well  known  to  require  illus- 
traticm.  So  also  in  attempting  to  scdve  unfamiliar  problems, 
in  mathematical  as  well  as  in  every-day  thinking,  we  often 
use  the  method  of  trial-and-error.  We  go  astray  a  few  timet 
before  striking  into  the  right  path.     Still,  in  the  end,  we 


332 


FALLAQES 


lit 


can  escape  error  almost  completely  in  this  field.  But  in  the 
case  of  natural  phenomena,  cc  nplete  obJectiTity,  as  we  have 
seen,  appears  to  be  out  of  our  power.  Successive  generations, 
can  appro:cimate  to  a  more  accurate  comprehension  of  the 
workings  of  nature,  but  a  full  comprehension  is  denied  us. 
We  use  models  which  never  quite  fit  the  concrete  circum- 
stances, and  our  empirical  interpretations  are  thus  neces- 
sarily infected  with  error.  To  some  slight  extent  our  best 
and  finest  efforts  at  understanding  the  world  in  which  we 
live  are  mistaken;  and  there  is  only  one  way  of  avoiding 
fallacy  in  this  field — viz.,  by  preserving  a  slightly  sceptical 
attitude  of  mind  towards  all  claims  of  finality.  To  recognise 
the  trap  is  to  avoid  falling  into  it,  and  while  our  thought 
In  tb'i  field  is  necessarily  imperfect,  it  is  not  necessarily 
fallacious.  It  would  be  fallacious  only  if  we  thought  we 
knew  in  cases  where  we  have  only  presumptive  evidence. 
There  is  no  fallacy,  so  long  as  we  maintain  the  Socratic 
attitude,  and  at  least  know  that  we  don't  know.  At  the  same 
time,  we  should  transcend  the  Socratic  pcsiticm  in  believing 
that  the  broad  basis  of  experience,  upon  which  our  modem 
science  rests,  enables  us  to  approximate  to  a  knowledge 
which  for  practical  purposes  is  becoming  progressively  more 
adequate. 

Source  of  Fallacy. — Prom  the  viewpoint  of  pure  logic,  there 
is  no  such  thing  as  error.  When  we  think  logically,  we  think 
truly,  and  it  is  only  so  far  as  we  fail  to  follow  the  rules  of 
pure  logic  that  we  deviate  into  fallacies.  A  purely  rational 
being  never  errs.  True,  perhaps, — but  then,  do  we  know  any 
purely  rational  beings?  Living,  as  we  do,  in  a  world  which 
we  experience  through  senses  which  are  easily  confused  and 
deceived,  and  with  a  memory  which  we  trust,  in  spite  of  its 
known  treachery,  only  because  we  have  nothing  better  in 
which  to  trust,  and  with  powers  of  self-deception  which  frame, 
as  valid  and  logical,  reasonings  which  are  mere  distorted 
reflections  of  instinctive  wants,  or  of  social  conventi(HiB  which 
have  long  since  lost  what  little  semblance  of  reason  they 
may  once  have  possessed — is  it  any  wonder  that  we  fall, 
time  and  again,  into  the  same  old  fallacies,  as  well  as  con- 
stantly blundering  in^o  new  ones? 

We  have  a  dual  nature.  On  the  one  hand,  we  have  the 
demands  of  a  lexical  reason,  voiced  in  the  ideal  conceptloni 
of  truth,  goodness,  beauty,  and  the  like.    On  the  other  hand 


TYPES  OF  FALLACY 


333 


we  have  the  mechanism  of  our  nervous  system,  with  its 
sense-organs  at  one  end  and  its  muscles  at  the  other,  an 
instrument  devised  for  practise  rather  than  theory,  cradled 
in  instinct  and  educated  in  custom,  and  Inherently  incapable 
of  satisfying  the  ideal  demands  of  pure  reason.  If  with  such 
an  instrument  we  believe  we  can  fulfil  the  v^emands  of  tran- 
scendent thought,  we  fall  necessarily  Into  fallacy.  The  only 
escape  from  this  ever-present  source  of  error  is  to  recognise, 
once  and  for  all,  that  perfect  satisfaction  of  these  ideel 
demands  is  out  of  the  question  for  beings  whose  sole  mech- 
anism for  fulfilling  such  demands  is  a  central  nervous  system 
developed  through  the  dark  ages  of  animal  evolution. 

The  utmost  we  can  do  is  so  to  organise  our  experience  as 
to  approximate  to  making  sense  of  it— to  bring  our  ideaia 
into  connection  with  the  facts,  and  to  elevate  the  brute  facts 
in  the  light  of  our  ideals,  as  far  as  this  may  be  possible, 
and  thus  create  a  science  and  a  mode  of  life  which  shall 
combine  actual  experience  and  Ideal  desire,  and  gradually 
and  progressively  approach  the  haven  where  we  fain  would 
be.  If  ^e  fully  recognise  this,  the  chief  source  of  fallacy 
will  be  removed.  If  we  know,  not  only  what  we  want,  but 
also  what  we  can  get,  we  are  not  likely  to  confuse  the  two. 
And  if,  avoiding  that  confusion,  we  go  to  work  to  create 
that  science  and  that  life  which  are  possible  for  us,  sub- 
stituting breadth  of  experience  where  depth  of  insight  seems 
denied  us,  we  shall  realise  the  fruits  of  the  Socratic  spirit, 
afad  shall  act  out  the  highest  llf^  which  is  in  our  power— « 
life  self-determined,  free,  and  raised  above  the  deeper  sources 
of  self-deception. 

Types  of  Fallacy.— There  are  no  special  types  of  fallacy. 
All  fallacies  partake  of  a  single  form— «i«.,  confusing  mental 
models  with  the  more  concrete  realities  of  experience,— and  all 
attempts  at  enumerating  and  classifying  typical  forms  of  fal- 
lacious thought  either  (1)  re-state  the  general  nature  of  fal- 
lacy, or  (2)  mention  some  special  occasion  of  possible  error. 
But  these  are  too  many  to  be  enumerated.  For  example,  the 
best  known  type  of  fallacy  is  what  is  called  Petitio  Principii, 
or  begging  the  question.  It  is  usually  illustrated  by  such 
examples  as  circular  definition,  or  as  the  explanation  of  some 
event  in  terms  of  itself.  E.  g.,  "A  cause  is  that  which  pro- 
duces an  effect,  and  an  effect  is  that  which  is  produced  by  a 
cause,"  "Wood  is  the  ligneous  part  of  trees,"  "The  poppy  (In 


•s- 


334 


FALLAQES 


H 


medicine)  tends  people  to  sleep,  quia  at  in  eo  virtus  dormi- 
tiva,"  "We  are  able  to  remember  what  has  happened  to  us 
because  we  possess  the  faculty  of  Memory,"  etc.  A  minor  type 
of  such  false  assumption  is  known  as  the  "fallacy  of  double 
question" — e.  g.,  "Have  you  decided  to  settle  down  to  a  decent 
kind  of  life  at  last?",  "What  have  you  done  to  your  coat?"  A 
second  well  known  type  of  fallacy  is  called  Ignoratio  Elenchi 
or  irrelevant  proof.  This  is  illustrated  by  brow  beating  a  wit- 
ness, attacking  the  personal  character  of  an  opponent,  or  rais- 
ing some  national  issue,  instead  of  arguing  on  the  facts  of 
the  case,  and  generally  by  appealing  to  prejudice,  hope,  and 
fear,  rather  than  to  reason.  But  it  is  easy  to  see  that  every 
instance  of  false  assumption  is  also  an  instance  of  irrelevant 
proof,  and  that  every  instance  of  irrelevant  proof  is  an  instance 
of  false  assumption.  In  fact,  we  have  here,  not  two  typical 
forms  of  fallacy,  but  two  statements  of  the  essential  nature 
of  all  fallacious  thought.  To  think  that  an  assumption  of 
ours  amounts  to  proof  is  lo  cotiuse  a  mental  model  with  the 
reality,  and  to  appeal  to  emotion  or  prejudice  rather  than  to 
reason,  is  to  attempt  to  substitute  a  subjective  mental  model 
for  an  objective  understanding  of  the  facts.  Such  attempts 
are  clearly  re-statements  of  the  essential  nature  of  fallacy  as 
such. 

So  too  the  celebrated  division  of  fallacies  into  two  classes, 
(1)  in  dictione,  and  (2)  extra  dictionetn — i.  e.,  fallacies  in 
language  rather  than  in  thought,  and  fallacies  in  thought 
rather  than  in  language,  respectively — breaks  down  in  the 
face  of  serious  criticism.  In  the  first  place,  the  distinction  is 
thoroughly  artificial— for  as  thought  expresses  itself  in  lan- 
guage, and  language  is  a  mere  vehicle  or  mental  model  for 
expressing  thought,  all  mistakes  in  language  are  due  to  mis- 
takes of  thinking.  Thus  the  typical  "fallacy  of  accent" — c.  g., 
"Saddle  me  the  ass.  And  they  saddled  him"-  could  not  pos- 
sibly arise  unless  there  were  some  inattention  of  thought  and 
thus  some  failure  to  grasp  the  meaning.  So  too  in  the  comic 
opera,  when  Patience,  who  "cannot  tell  what  love  may  be,'' 
mentions  that  she  once  had  a  beloved  playmate,  "and,  by  the 
way,  he  was  a  little  hoy,"  the  Chorus  Immediately  reply  that 
they  "thought  as  much— he  was  a  little  boy."  Patience  rejoins, 
"Remember,  pray,  he  was  a  little  boy."  The  variations  of 
accent  follow  the  variations  of  meaning,  and  it  is  impossible 
to  separate  the  words  from  the  thought.    In  the  second  place, 


TYPES  OF  FALLACY 


335 


If  we  admit  that  linguiBtlc  usage  it  at  times  misleading,  as  in 
the  famous  oracle.  "Pyrrhus,  I  say.  the  Romans  can  subdue." 
such  ambiguities  of  accidence  or  syntax  are  but  single  occa- 
sioDs  of  error,  and  are  as  nothing  when  compared  with  the 
vast  and  unclassified  field  of  such  occasions.  If  we  wish  to 
avoid  a  fallacious  and  superficial  clearness,  we  shall  refuse 
to  "^tempt  a  classification  of  these  special  occasions  of  error, 
an  >aall  assert  that  all  fallacies  belong  to  a  single  type — vie., 
tht)  confusion  of  mental  models  with  realities  or  with  other 
mental  models. 

FOR  rURTHBB  RBADINO 

W.  R.  Boyce  Gibson,  The  Problem  of  Logic,  chapter  xxxUL  H. 
Plato,  £«(/it/<t6m««.  Lotze,  Logic,  Bk.  II,  chapter  t1.  J.  O.  Hibben, 
Logic,  Part  II,  chapter  xvl. 


BXBRCISB8 

Are  the  foH-'Wlng  argumeota  fallacioua,  and.  If  so,  in  what  does 
the  fallacy  consist:  (1)  "Who  rules  o'er  freemen  should  himself  be 
free"?  You  might  as  weil  say.  Who  drires  fat  oxen  should  himself 
be  fat!  (2)  It  is  a  mistake  to  say  that  the  best  Judges  in  matters 
of  art  are  always  In  a  minority.  For,  consider — suppose  it  true  that 
the  minority  are  always  the  best  Judges,  and  carry  it  to  extremes. 
Hie  smallest  minority  consists  of  one  man.  If  the  principle  ts  true, 
then  each  man  will  himself  be  the  best  Judge,  and  there  will  be  as 
many  best  Judges  as  there  are  indlTlduals  who  differ  from  others,  and 
thus  constitute  extreme  minorities.  But  this  is  absurd.  Therefore, 
tlie  majority  are  always  the  t>eet  Judges.  (3)  Let  x  =  a,  then  ax 
=  a>,  and  ax  —  x2  =  a*  —  xa  i.  e.,  x(a  — x)  =  (a  +  x)  (a  — x),  and 
1^  cancelling,  z  =  a  +  z.  i  e-.  x  =  2z,  or  1  =  2.  (4)  I  am  a  Chlan, 
and  no  Chian  can  open  tats  lips  without  telling  a  lie.  llieretore  I 
lied  wben  I  said  I  was  a  Chian,  etc.,  so  that  I  am  not  a  Cblan — In 
witi(^  case,  perhaps,  I  told  the  truth,  and  thus  am  a  liar  aiftar  alL 
(8)  Other  people  cannot  be  as  sensitlTe  «a  I  am ;  for  they  do  not 
make  tlie  same  fnaa  about  their  feelings  aa  I  do.  (6)  Ur.  X  Is  a 
sound  man  for  Benatw,  Cor  he  made  an  excellent  after-dinner  speech 
the  oitber  erening.  (7)  I  could  be  a  great  artist.  If  It  were  not  for 
my  environment:  for  I  feel  it  within  me.  (8)  Mr.  Z  Is  not  to  be 
trusted  as  mayor  for  his  table  manners  leave  n     h  to  be  desired. 


CHAPTER  XXXI 
THE  SYSTEM  OF  THE  SCIENCES 

In  periods  of  scientific  development,  a  tendency  arises  in  the 
direction  of  applying  scientific  method  in  somewhat  narrow 
channels,  and  perhaps — in  view  of  the  vast  body  of  scientific 
knowledge  and  the  exacting  requirements  of  modern  technique^ 
— such  specialisation  is  Inevitable.  Inevitable  or  not,  how- 
ever, it  is  certainly  the  tendency,  and  the  modern  student, 
after  years  of  study,  sometimes  complains  of  bewilderment. 
He  cannot  see  the  wood  for  the  trees,  and  feels  a  need  for 
breadth,  as  well  as  depth,  of  vision.  He  wishes  to  form  a 
mental  picture  of  experience  as  a  whole,  and  not  only  of  what 
he  sees  through  his  microscope  or  in  his  test-tube.  In  answer 
to  this  dissatisfaction  and  vaguely  formulated  demand,  there 
have  arisen  attempts  to  systematise  the  results  and  principles 
of  the  various  departmental  sciences,  and  thus  to  give  a  single 
world-picture  which  shall  be  just  to  all  the  chief  discoveries 
of  science,  and  shall  at  the  same  time  satisfy  the  craving  of 
the  mind  for  unity  and  totality.  The  best  known  examples 
of  such  attempts  are  found  in  the  "Synthetic  Philosophy"  of 
Herbert  Spencer,  and — to  a  lesser  extent — in  the  more  exact 
but  not  less  unwieldly  tomes  of  Wilhelm  Wundt.  On  a  minor 
scale,  however,  most  modern  writers  on  logic  attempt  to  draw 
together  the  various  lines  of  inquiry  and  envisage  them  as  a 
whole. 

Nature  of  Such  Systematisation. — Such  systematisation  is, 
in  the  first  place,  a  last  and  most  gigantic  attempt  at  analysts 
and  synthesis.  We  wish  to  take  all  knowledge  for  our  prov- 
ince and  put  it  together.  That  is  synthesis.  We  wish  also  to 
put  it  together  In  a  way  so  articulate  and  organised  that  we 
can  see  the  inter-relation  of  the  parts  in  the  light  of  the  whole. 
That  is  (partly)  analysis.  We  wish  our  system  to  be  both 
analytic  and  synthetic. 


1  Tbla  U  true  not  only  of  laboratory  sclencM  like  ^yrica  and 
chemiiitry,  but  also  of  the  social  and  lln(rul<itlc  sciences.  History  and 
ptillology  have  tbelr  technique  as  well  as  microscopy  and  blatology. 

336 


AIM  OF  SUCH  SYSTEMATISATION 


337 


In  the  second  place,  luch  lystemB  are  both  abatract  and 
determinate.  They  are  abstract  It  ii  imponible  for  one 
man  to  carry  in  his  head  at  one  and  the  same  time  all  the 
detail  of  science,  and  consequently  the  world-picture  which  we 
desiderate,  will  have  to  be  largely  in  outline.  That  is  to  say. 
it  will  necessarily  be  abstract.  Medieval  metaphysics,  which 
largely  follows  the  conception  of  Aristotle,^  is  highly  abstract 
According  to  this  conception,  we  pass  from  the  more  concrete 
and  detailed  knowledge  to  the  higher  or  "first"  principles, 
simply  by  leaving  out  the  detail  and  retaining  the  bare  out- 
line. The  highest  and  intellectually  most  abstract  of  all  is 
the  concept  of  Being,  and  the  chief  function  of  a  system  of 
first  principles  is,  from  this  viewpoint,  to  study  the  nature  of 
Being  qua  Being — apart  from  its  specific  differentiations  in 
the  wealth  of  detail  which  we  find  in  nature.  A  man,  month, 
mountain,  nation,  wind,  all  are,  or  have  Being.  But  they  have 
different  kinds  of  Being.  The  kind  of  Being  which  a  month 
has  is  very  different  from  the  kind  of  Being  which  a  man  has, 
or  even  which  a  mountain  has.  The  science  of  ontology,  how- 
ever, was  intended  to  abstract  from  all  these  differences,  and 
deal  with  the  concept  of  bare  Being.  It  is  easy  to  see  that 
the  final  world-picture  in  terms  of  pure  Being,  would  turn 
out  to  be  the  barest  of  bare  skeletons,  with  all  the  life  and 
color  gone. 

In  more  modern  times,  however,  and  especially  since  the 
work  of  Hegel,  thinkers  have  tended  to  regard  the  picture  of 
the  whole  as  more  determinate  and  concrete,  and  to  view  the 
isolated  fragments  of  the  system — particular  elements  of  expe- 
rience— as  thin  and  poor  in  content,  iiv  short  as  abstract  For 
the  modem  viewpoint,  a  concept  is  not  abstract  qua  intel- 
lectual, and  concrete  qua  sensory,  but  is  abstract  qua  fragmen- 
tary, and  concrete  as  seen  in  its  place  in  a  totality.  For  this 
view  the  concept  of  Being  is  not  the  poorest  and  most  empty 
of  content  but  the  richest  and  fullest  of  all  contents.  It  con- 
tains within  Itself  the  principle  of  determination  of  all  the 
specific  forms  of  Being,  and  instead  of  being  an  abstract  skele- 
ton, made  up  of  only  the  single  element  common  to  all  entities, 
is  the  richest  of  all  beings,  containing  as  it  does  the  infinite 
variety  of  nature,  and  all  possible,  as  well  as  all  actual,  details. 
It  is  produced  by  addition  rather  than  by  substraction,  and  is 

1  Ariatotie'a  view  !■  developed  In  the  JTetapkyHca.  Cf.  In  partloriar, 
Met  I,  I. 


338 


THE  SYSTEM  OF  THE  SCIENCES 


f 


I 


!^ 


the  Bum-total  of  Reality,  the  Absolute  or  ent  realittimum.s 
It  la  thus  the  moat  concrete  and  determinate  of  concepts, 
though  It  la  atlll  regarded  aa  partly  abatract.^ 

In  the  third  place,  auch  a  ayatem  la  the  final  work  of  indue- 
tlon  and  deduction.  It  la  to  be  the  final  mental  model  of  the 
universe,  and  ah&uld  sum  up  in  Itself  all  the  preceding  labor 
of  analysis  and  synthesis,  abstraction  and  determination,  by 
proceeding  to  determine,  aa  far  aa  possible,  the  law  of  the 
Whole.  It  la  uaual  to  regard  this  law  aa  the  law  of  Reaaon,  a 
principle  of  organiaation,  by  means  of  which  the  whole  uni- 
verse la  regarded  aa  a  vast  Individual,  containing  within  Itself 
both  Identity  and  difference.s 

Finally,  it  is  possible  also  to  regard  auch  a  ayatem  aa  a  aln- 
gle  gigantic  definition  or  aa  a  final  claaaification,  and  this 
view  has  exercised  considerable  infiuence  upon  the  work  of 
Spencer  and  Wundt.  Such  attempta  at  classification  have  been 
very  numerous,  and  we  shall  consider  some  of  the  best  known 
typea  later.  In  general,  then,  we  can  aay  that  the  nature  of 
such  ayatematisatlon  is  to  complete,  at  least  in  general  out- 
line, the  work  of  investigation  and  expoaition,  to  round  it  oft 
in  some  way,  ao  that  the  apecialiat,  at  work  upon  his  partic- 
ular portion  of  the  whole,  may  also  form  a  mental  picture  of 
the  whole,  and  may  thus  realise  hia  unity  and  fellowship  with 
his  co-workera  in  other  parts  of  the  field. 

Aim  of  Such  Systematlsatlon  (A)  Objectivity. — ^The  aim 
of  auch  ayatematiaation  la  not,  however,  merely  to  frame  a 
single  model  of  the  whole,  so  that  the  specialist  may  not  feel 
lost  or  cut  off  from  his  fellows.  We  aim  at  something  more 
than  a  cure  for  intelleotual  Heimtoeh.  In  actual  fact,  almost 
everyone  frames  some  sort  of  idea  of  experience  as  a  whole, 
of  the  meaning  and  ve  le  of  life,  and  of  the  place  of  man  in 
the  universe — i.  e.,  reacts  in  some  way  to  what  have  been 
called  the  Great  Problems.  These  reactions,  however,  tend  to 
be  somewhat  arbitrary  and  subjective,  and  refiect  a  somewhat 
narrow  and  eclectic  viewpoint  Optimism  and  pesiimism,  for 
instance,  are  ordinarily  somewhat  shallow,  and  have  little 
hold  upon  objective  facts.  They  are  usually  prejudices,  rather 
than  scientifically  tested  modela,  and  the  aim  of  scientific 


li  I 


»Cf.  G.  Slsuttft],  Hauptprohh    j  der  PhUotophie,  cbspter  I, 
Bradley,  Appearance  and  Realitu.  Part  II. 
*  C(.  H.  Joachim.  The  Nature  of  Truth,  tut  ch«irt»r. 
B  Cf.  F.  H.  Bradley,  PrtmeipUa  of  Logtc,  (^.  44»-4B0. 


F.  H. 


AIM   OF  SUCH  SYSTEMATISATION 


$39 


i/ 


exposition  in  sjntematiBing,  precisely  as  in  defining  or  classi- 
fying, is,  before  everything  else,  to  be  objective.* 

It  is  not  merely  to  satisfy  our  craving  for  anity  and  totality 
of  outlook,  that  we  systematise.  For  that  craving  can  be  sat- 
isfied by  almost  any  sort  of  mental  model.  Every  religion, 
every  code  of  thought  current  in  artistic,  commercial,  charit- 
able, and  family  circles.  Las  its  own  solution  of  this  problem, 
and  such  solutions  are  found  fairly  satisfactory,  so  far  as  the 
needs  of  such  circles  go.  But  the  scientifically  minded  man 
wants  something  more  than  the  mere  satisfaction  of  a  sub- 
jective desire — he  wants  to  know  the  facts.  He  wishes  his 
system  to  be  satisfactory,  not  merely  to  himself,  in  a  sub- 
jective way,  as  a  kind  of  registering  of  his  private  and  unstand- 
ardised  reaction  to  the  universe  as  he  happens  to  experience 
it.  He  wishes  his  system  to  be  objectively  valid,  and  to  be 
true  of  experience  as  a  whole.  For  Instance,  many  people 
regard  the  whole  universe  as  revolving  around  themselves  or 
the  interests  of  their  immediate  friends  or  profession.  This  is 
a  narrow  and  prejudiced  view,  and  the  aim  of  scientific  expo- 
sition is  at  something  more  all-inclusive,  and  more  definitely 
in  contact  with  objective  facts  and  objective  laws.  The  first 
aim,  then,  of  such  attempted  systematisation,  is  objectivity. 

(B)  Completeness. — In  the  second  place  we  aim,  here  if 
anywhere,  at  completeness.  A  partial  or  one-sided  view  is  here 
wholly  out  of  place.  Aut  totum,  aut  nihil.  The  materialistic 
view  of  the  universe,  for  instance,  is  one-sided  and  incomplete. 
Viewing  all  reality  as  matter  in  motion,  and  all  science  as 
specialised  effort  to  solve  special  problems  of  moving  matter, 
it  tends  to  leave  out  all  the  characteristic  work  of  the  mental 
and  moral  sciences,  and  is  of  very  little  use  as  a  working 
hypothesis  in  the  historical  and  philological  sciences.  It  is 
incomplete,  and  thus,  as  a  view  of  the  whole,  is  a  travesty  of 
the  fact8.7  So  too  the  study  of  truth-values,  such  as  we  have 
in  logic  and  in  the  natural  sciences,  is  one-elded,  unless  atten- 
tion is  paid  also  to  the  ethical,  esthetical,  and  religious  valu- 
ings,  and  a  purely  theoretical  view  of  the  whole  is  unjust  to 
three-fourths  of  life — ^Just  as  perhaps  a  purely  practical  view 
of  the  whole,  or  a  view  purely  esthetical,  is  equally  incom- 

9  Of.  A.  r».  Trf^T^'jny'ft  pr<>«W<»ntl8l  jMtdrojw  to  the  Am*rif«n  PhHo- 
•ophical  Association,  Phifoaophical  Rerteic,  Vol.  XXVI,  1917,  pp.  123- 
163. 

1  For  a  clear  exposition  of  materialism,  see  BUchner,  Matter  and 
Bnergt/. 


340 


THE  SYSTEM  OF  THE  SCIENCES 


plete.8  In  attempting  to  let  up  a  mental  model  which  ahall 
represent  the  universe  as  a  whole,  it  is  necessary  to  be  at 
least  as  complete  as  is  possible,  and  to  leave  unrepresented  no 
class  of  experiences,  no  view  of  the  facts,  however  distorted. 
The  idea  of  the  whole  must  be  oll-embraclng — i.  e.,  must  be 
complete. 

How  Far  Realisable? — How  far  can  we  put  together  the 
various  lines  of  scientific  effort,  and  systematise  them  so  as  to 
present  a  world-picture  which  shall  be  both  objective  and  com- 
plete? It  is  not  difficult  to  see  that  this  ca.anot  be  wholly 
accomplished.  In  the  first  place,  our  sciences  are  not  wholly 
objective.  They  consist  of  mental  models  which  do  not  per- 
fectly correspond  to  the  facts,  but  are  in  a  process  of  trans- 
formation which  renders  them  ever  more  and  more  acceptable 
from  an  objective  point  of  view.  Where  complete  objectivity 
is  not  to  be  found  in  the  data  to  be  synthesised,  complete 
objectivity  can  hardly  be  expected  in  the  total  picture.  In 
the  second  place,  no  single  science  is  anything  but  incom- 
plete, and  it  Is  not  held  that  the  subjects  of  scientific  Inquiry 
will  ever  be  completely  understood.  Here  also  we  have  only 
approximation  towards  our  goal,  and  here  also  we  must  admit 
that  if  the  data  are  incomplete,  the  whole  which  is  to  be  con- 
structed out  of  such  data  must  itself  be  at  least  equally  incom- 
plete. A  synthesis  of  our  various  lines  of  scientific  Inquiry, 
then,  cannot  be  wholly  objective  and  cannot  be  wholly  com- 
plete, in  the  sense  of  giving  us  a  final  world-picture.  This 
has  become  so  well  known,  that  at  the  present  day  the  idea  of 
constructing  such  a  world-picture  has  been  abandoned,  and  in 
its  place  It  is  proposed  merely  to  attempt  to  put  together  our 
mental  models  and  instruments  of  investigation  In  a  way  which 
shall  be  Just  to  them — t.  e.,  to  relate  the  sciences.  Imperfect  as 
they  are,  to  one  another,  and  to  discover.  If  possible,  the 
relation  of  historical  Inquiry  to  philosophical  or  to  palaeonto- 
loglcal  research,  or  the  relation  of  histology  to  botany  and 
zoology,  or  the  relation  of  psychology  to  the  whole  field  of 
scientific  inquiry,  etc.  In  a  word,  the  aim  Is  no  longer  to 
present  a  final  picture  of  the  world  as  it  is — for  no  one  man 
and  no  group  of  men  has  the  requisite  knowledge — but  rather 
to  systematise  the  sciences  as  we  have  them  at  the  present 
day,  and  thus  to  understand  the  interrelation  of  our  own 


8  Cf.  Varlsco,  The  Great  Prohlemt,  pp.  26-27,  286  ff..  Appendix  V. 


/ 


TYPES  OF  SUCH  SYSTEMATISATION 


341 


metbodi  and  mental  models.  As  this  inquiry  is  definitely  and 
explicitly  confined  to  the  world  of  mind-made  entitles,  we  can 
approart-  it  with  more  confidence.  In  principle,  at  any  rate, 
it  should  be  capable  of  realisation. 

Types  of  Such  Systematlsation.— In  the  history  of  science, 
there  have  been  many  attempts  at  such  systematisatlon,  at 
embracing  the  worlc  of  science  as  a  whole  and  viewing  It  from 
a  single  standpoint.  One  of  the  most  famous  is  the  system  of 
Plato.  He  has  (1)  a  general  view  of  the  whole  field  of  human 
knowledge,  and  (2)  a  special  view  of  me  field  of  scientific 
Inquiry.  The  general  view  la  known  as  the  "four  stages  of 
Intelligence."  and  is  symbolised  in  the  accompanying  diagram. 
In  the  lowest  atoge  of  lntelligc/>ce.  we  have  the  attitude  of 
uncritical  acceptance  of  any  and  every  view,  devoid  of  the 
faintest  vestiges  of  scientific  metiiod.  In  the  second  stage  we 
have  the  attitude  of  practical  common-sense,  which  tests  the- 
ories only  in  the  light  of  their  Immediately  practical  work- 
ings. In  the  third  stage  we  have  what  we  should  call  the  field 
of  the  departmental  sciences.  Things  which  we  can  touch  and 
see  are  here  dealt  with  only  so  far  as  they  throw  light  upon 
laws  in  some  department  of  scientific  inquiry,  and  the  Interest 
in  this  field  Is  an  interest  In  law.  rather  than  in  things  or 
opinions.  In  the  fourth  and  final  stage,  an  attempt  is  made^i 
to  transcend  the  limitations  of  the  departmental  sciences  and^ 
construct  an  undepartmentalised  view  of  reality  as  a  whole,', 
by  the  use  of  pure  reason.    This  is  the  field  of  metaphysics.    J 

So  much  for  the  general  view  of  human  knowledge.  The 
third  stage,  which  contains  the  field  of  science,  is  divided  up 
in  accordance  with  the  principle  of  passing  from  the  simple 
to  the  complex,  and  turning  the  soul  from  the  changeable  to 
the  permanent  and  eternal.  First  we  have  arithmetic,  then 
plane  geometry,  solid  geometry,  astronomy,  and  harmony,  and 
finally  a  study  of  the  mutual  association  and  relationship  of 
these  sciences,  which  teaches  us  the  ties  which  bind  them 
together— what  we  might,  perhaps,  call  epistemology.  This 
bridges  the  way  to  the  science  of  sciencee,  dialectic,  which 
corresponds,  in  a  rough  and  approximate  way,  to  what  we 
have  recognised  as  the  field  of  transcendent  Judgments.' 

The  number  of  sciences  thus  recognised  by  Plato  is  extremely 
gmall — ^"Imperfect"    and    empirical    sciences    are    expressly 

•  Cf.  PUto'a  RepuhUe,  from  the  last  few  pagea  of  Bk.  VI  to  half 
way  tiiroacli  Bk.  VII. 


(''' 


r  .^  ■•" 


342 


THE  SYSTKM  OF  THK  SCH-NCES 


P««rtk   Btasc 

Dialectic  or   Metaphyalcs 


Tklrd    St«s« 

Science 


SeeoBd  It  tmg9 
Common   Sense 


lowest  S«aB« 


KplBtemolosy    (7) 
Harmony 
\atronomy 
Solid    QeomMry 
Plane  Qeometry 
Arithmetic 


excluded  from  his  scheme — and  all  belong  to  a  single  group, 
the  mathematical  group,  which  leads  on  to  epistemology  and 
metaphysics.  The  philological,  social,  and  historical  scimces 
find  no  place  in  the  scheme.io  and  the  sciences  which  he  does 
admit,  are  admitted  only  on  the  ground  that  they  are  busied 
with  the  eternal  rather  than  with  the  empirical,  and  are  thus 
adapted  to  turn  the  eye  of  the  soul  away  from  the  world  of 
sense-perception,  and  to  develop  our  powers  of  "pure"  rea- 
soning. 

This  view  has  been,  and  still  is,  extremely  important  in  its 
influence  upon  religious  minds,  and  upon  the  minds  of  those 
who  are  especially   interested  In  the  ideal  development  of 

"Plato  do«.  perhaps,  recognise  political  science,  but  tbto  repreMats 
the  practical  application  of  JlaJectlc.  and  hardly  finds  a  place  In  the 
third  stage  of  Intelligence. 


V 


VALIDITY  OF  SUCH  SYSTEMATISATION 


J43 


humanity.  But  from  the  potnt  of  view  of  the  tctentiit  who 
wlahee  to  be  Jutt  to  all  lines  of  sclentlflc  inquiry,  It  la  clearly  - 
unsatisfactory.  It  ii  neither  objective  nor  complete,  and  the 
reason  for  Its  failure  to  solve  our  problem  is  to  Im  sought  In 
the  fact  that  the  vi9wpolnt.  from  which  the  different  lines  of 
Inquiry  aia.  uaited,  is  external,  and  belongs  to  a  thtory  of  the 
ideal  nature  of  man,  rather  than  to  Bclentiflc  research  Itself. 

As  representative  of  more  modern  attempts  to  solve  this 
problem,  it  will  be,  perhaps,  sufflctent  to  consider  the  scheme 
of  "Wuadt.  As  will  be  seen  from  the  accompanying  diagram,  it  - 
attempts  to  be  both  objective  and  complete,  and  to  give  a 
mental  picture  of  the  interrelation  of  all  lines  of  actual  scien- 
tific inquiry. 

Vatidity  of  Such  SysUmatlsation.— Complete  validity  In 
such  attempts  at  systematlsatlon  is  hardly  to  be  looked  for. 
The  nature  of  the  attempt  to  systematise  is  largely  descrip- 
tive. And  to  describe  accurately  and  completely  the  relation 
of  the  various  sciences  to  one  another  is  hardly  possible.  The 
reason  for  this  is  to  be  sought  in  the  fact  that  there  are,  at 
the  present  day,  no  final  or  hard  and  fast  lines  of  distinction. 
The  botanist  has  to  be  something  of  a  chemist  and  mathema- 
tician. He  frequently  has  to  know  something  of  geography, 
geology,  and  soology,  something  of  the  general  theory  of  evolu- 
tion, and  sometimes  even  of  psychology  and  logic.  So  too  the 
psychologist  requires  knowledge  of  biology,  of  physics,  and  of 
sociology,  as  well  as  of  mathematics.  Every  specialist  uses, 
in  actual  practise,  whatever  he  finds  necessary  to  the  solution 
of  his  (fecial  problem,  regardless  of  its  place  in  the  "system," 
Just  as  the  comparative  anatomist  pays  little  or  no  attention 
to  the  system  which  we  find  in  zoology.  Where  the  work  of 
scientists  thus  cuts  across  any  lines  which  the  systematiser 
may  draw,  it  is  plain  that  description  of  the  work  of  science 
can  hardly  be  expressed  In  any  of  the  typical  systematic 
forms,  if  we  wish  to  be  objective  In  our  description.  Complete 
validity,  then,  is  out  of  the  question. 

What  the  systematiser  cob  aim  at,  however,  is  a  reasonable 
completeness,  and  at  some   principle  of  organisation  which 
makes  his  system  convenient  for  purposes  of  reference.    Such  y 
a  system  as  Wundt's  certainly  fulfils  this  aim,  and  is  so  far  s 
to  be  regarded  as  valid.     But  it  remains  sufficiently  obvious  ' 
that  any  such  system  must  be  arbitrary  and  from  many  view- 
points unsatisfactory;  and  if  we  keep  in  mind  the  concrete 


11 


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l/ 


SUMy\RY 


345 


needs  of  scientific  research  i  ■scientific  exposlUon,  we  shall 
see  that  no  one  system  can  p  Jly  be  regarded  as  final,  even 
for  purposes  of  reference,  Fo  example:  for  certain  purposes 
a  group  of  Medical  Sciences  Is  advisable,  and  for  certain  other 
purposes  a  group  of  Social  Sciences.  Yet  neither  of  these 
demands  receives  satisfaction  from  such  a  system  as  that  of 
Wundt.  All  that  we  can  hope  for,  then,  In  this  field.  Is  a 
system  which  shall  present  us  with  a  general  view  of  the  work 
of  science,  In  a  way  which  Is  fairly  accurate  and  reasonably 
complete.  Complete  validity,  however,  even  In  the  case  of 
thia  purpose,  is  not  to  be  expected. 

Summary.— So  far  we  have  seen  that,  in  answer  to  cer- 
tain needs  arising  in  an  age  of  over-speclallsatlon,  attempts 
are  made  so  to  systematise  the  special  sciences  as  to  present 
us  with  a  general  world-picture.  This  attempt  is  eventually 
given  up  as  unscientific  at  the  present  stage  of  knowledge,  and 
In  its  place  we  try  to  arrange  the  lines  of  actual  scientific 
inquiry  in  such  a  way  as  to  obtain  a  general  view  of  the  work 
of  science.  This  too  is  found  to  be  unsatisfactory  in  point  of 
objectivity  and  completeness,  and  the  only  purpose  which  it 
can  reasonably  be  expected  to  serve  is,  convenience  for  refer- 
ence. This  aim  also  cannot  be  completely  accomplished,  but 
systems  such  as  that  of  Wundt  are  at  least  helpful  and  sug- 
gestive. 

FOR  FURTHER  READING 

J.  O.  Htbben.  Logic.  Part  II,  chapter  xvll.  Herbert  Spencer,  CUuti- 
llcatUm  of  the  Science*.  W.  Wundt,  Logik,  (3rd  Edit.),  Vol.  II,  pp 
8B-100. 


J 

I 


CHAPTER  XXXII 


i! 


THEORY  OP  SCIENTIFIC  METHOD 

The  Problem.— So  far  we  have  discussed  in  detail  the 
chief  characteristics  of  scientific  method,  whether  for  pur- 
poses of  investigation,  or  for  purposes  of  exposition.  It  now 
remains  to  put  together  what  we  have  discovered,  and  to 
formulate  a  general  theory  of  scientific  method,  comparable 
to  the  theory  of  Judgment  and  the  theory  of  inference  dis- 
cussed above.  The  general  nature  of  scientific  method  plainly 
consists  in  framing  some  mental  model  or  hypothesis  in  ref- 
erence to  a  giveu  situation,  and  then  attempting  to  under- 
stand the  situation  in  terms  of  the  mental  model,  or  of  some 
modification  of  that  model  introduced  after  further  reference 
to  the  given  situation.  All  that  we  really  understand  or  are 
able  to  take  into  our  mental  grasp  is,  in  the  last  analysis,  the 
structure  of  the  mental  model  itself;  but  we  can  make  this 
progressively  more  adequate  by  continued  reference  to  the  con- 
crete situation.  This  "reference"  takes  place  by  means  of 
sense-perception.  There  are  thus  two  factors  in  the  use  of 
scientific  method,  (1)  the  sensory,  by  which  we  are  able  to 
keep  in  some  sort  of  touch  with  the  natural  environment,  and 
(2)  the  intellectual,  by  means  of  which  we  construct  and 
modify  our  mental  models.  To  frame  a  "theory"  of  scientific 
method,  it  will  be  necessary  to  treat  each  of  these  factors  sep- 
arately, before  taking  them  together,  and  to  treat  them  in  two 
ways.  In  the  first  place  we  shall  state  what  part  they  actually 
do  play,  and  by  this  description  answer  the  question  of  fact. 
In  the  second  place  we  shall  examine  briefly  the  objectivity 
and  completeness  of  the  results  so  attained,  and  by  this  criti- 
cism answer  the  question  of  validity. 

The  Sensory  Element  in  Scientific  Method.  (A)  Mind- 
Made  Entitles. — In  the  case  of  mind-made  entities,  sense- 
perception  plays  a  very  minor  role,  but  still  a  role  which  is 
both  appreciable  and  necessary.  In  experimenting  with  a 
Jig-saw  puzzle  or  a  cipher,  the  sense  of  sight  plays  an  appre- 
ciable part,  and  the  sense  of  touch  may  also  come  into  play. 

346 


THE  INTELLECTUAL  ELEMENT 


347 


In  solving  mathematical  or  ethical  problems,  many  sensuous 
elements  appear  to  be  indispensable,  though  they  are,  of  course, 
in  no  sense  final.  Elements  other  than  sensory  play  the  chief 
part,  but  here  also,  as  iu  the  case  of  natural  phenomena,  sen- 
suous perception  is  a  condition  without  which  we  could  have 
no  scientific  knowledge,  and  its  function  is,  to  keep  us  in 
touch  with  the  concrete  situation,  whatever  that  may  be. 

(B)  Natural  Phenomena.— In  dealing  with  natural  phe- 
nomena, it  is  only  by  means  of  sense-perception  that  we  become 
aware  of  them.  It  Is  only  by  means  of  our  senses,  sight,  hear- 
ing, and  the  rest,  that  the  physical  world  is  given  to  us  in  the 
form  of  concrete  situations.  We  build  houses  out  of  materials 
which  we  can  touch,  see,  and  handle.  The  earth  on  which  we 
live,  the  rain  and  sun,  the  changing  seasons — even  our  books, 
music,  and  art — all  these  are  given  to  us,  in  the  first  place, 
by  way  of  sensuous  perception.  And  yet,  sensation  plays  no 
final  part.  The  world  of  physical  science  is  very  different 
from  the  sensations  of  color,  sound,  and  contact,  with  which 
our  sense-organs  respond  to  stimulation.  Sensation  is  only 
one  element  in  scientific  method,  and  its  function  is  to  furnish 
us  with  a  starting-point,  a  concrete  situation  which  we  can 
proceed  to  analyse  and  synthesise,  etc.,  until  our  intellectual 
aspirations  are  satisfied,  so  far  as  this  is  possible. 

The  intellectual  Element  (A)  Mind-Made  Entitle*.— In 
scientific  method,  the  part  played  by  intellectual  elements  is 
far  more  in  evidence.  The  whole  matter  of  constructing  mental 
models,  and  deducing  consequences  from  the  general  plan  of 
such  models,  is  a  matter  for  the  intellect.  The  way  in  which 
these  models  are  constructed,  however,  has  perhaps  not  been 
made  sufltciently  clear.  They  are  constructed,  in  every  case, 
by  applying  the  Intellectual  standards  of  identity,  difference, 
and  organisation,  internal  and  external,  so  far  as  such  appli- 
cation proves  to  be  possible.  The  case  of  analysis  and  syn- 
thesis has  been  dealt  with,  at  least  in  principle,  in  an  earlier 
cbapter.i  In  the  case  of  abstraction,  it  is  still  more  obvious 
that  in  singling  out  for  special  attention  some  one  element  or 
aspect  of  the  situation  which  results  from  analysis,  we  are 
applying  the  standard  of  identity,  and  that  in  excluding  from 
consideration  every  element  or  aspect  ofnor  than  the  one  espe- 

» Chapter  xtI,  wliere  analrai*  and  »yft''io«l»  are  dealt  with,  In  prin- 
ciple, under  the  he«dlng  of  "analytical  expanalon"  and  '■aystematlc 
conatructlTeneM,"  reapectlvely. 


348 


THKORY  OF  SCIKNTIFIC  METHOD 


daily  aelected,  we  are  applying  also  the  standard  of  differ- 
ence. So  also  in  the  case  of  determination.  We  determine  a 
single  element  or  aspect  by  placing  it  experimentally  in  a 
number  of  contexts,  each  of  which  is  different,  and  each  of 
which  adds  a  new  determination  to  the  single  element  with 
which  we  started.  In  this  case,  it  is  sufBclently  obvious  that 
the  standards  of  Identity,  difference,  and  organisation  are 
being  used.  Finally,  In  the  case  of  induction  and  deduction — 
elaborate  methods  which  use  every  resource  of  the  preceding 
methods  In  establishing  some  law— it  should  be  sufficiently 
plain  that  the  same  standards  are  being  used,  though  in  a  way 
which  is  more  complex,  as  the  situation  and  the  methods 
employed  are,  as  a  general  rule,  more  complicated.  So  too 
definition  usually  Involves  some  kind  of  statement  of  what 
the  object  defined  is,  and  some  distinction  of  It  from  objects 
which  are  like  it  but  are  regarded  as  different;  and  classifi- 
cation is  very  definitely  an  organisation  or  system  which  con- 
tains a  number  of  differentiated  elements,  each  of  which  may 
be  regarded  as  an  identity.  So  too  proof  proceeds  by  construct- 
ing a  mental  model  which  represents  the  situation  to  be 
proved.  This,  like  all  mental  models,  is  a  little  system  built 
up  out  of  elements  which  are  mental  counters,  differentiated 
identities,  and  the  same  standards  govern  our  constructions  In 
the  case  of  proof  as  in  the  previously  mentioned  cases. 

(B)  Natural  Phenomena.— With  natural  phenomena  we 
deal,  as  we  have  already  seen.  Indirectly.  We  construct  mental 
models  in  the  form  of  hypotheses,  and  by  trying  out  one  of 
these  after  another  come  as  close  to  understanding  the  nature 
of  such  phenomena  as  we  can.  In  constructing  these  mental 
models  we  use  the  same  intellectual  standards  of  identity, 
difference,  and  organisation,  to  which  we  have  already  referred 
in  the  case  of  mind-made  entitles,  and  in  general,  the  part 
played  by  intellectual  elements,  considered  by  themselves.  Is 
approximately  the  same  in  the  two  cases.  It  is,  in  fact,  only 
in  relation  to  sensory  elements  that  a  difference  can  be  estab- 
lished. This  difference  consists  in  the  fact  that  problems  con- 
cerned solely  with  mind-made  entitles  can  as  a  rule  be  com- 
pletely solved,  while  problems  concerned  with  natural  phe- 
nomena cannot  be  completely  solved.  That  Is  to  say,  "ur 
mental  model  may  be  the  mind-made  entity  itself — the  object 
studied,  and  the  model  in  terms  of  which  we  approach  the 
study  of  It  may  completely  coincide.    But  In  the  case  of  nat- 


li!k; 


THE  INTELLFXTUAL  ELEMENT  «• 

ural  phenomena,  such  coincidence  Ib  an  ideal  toward,  which 
we  can  progressively  approximate-but  some  gap  always 
remains.  So  far.  then,  as  the  construction  of  mental  modd. 
a.  such  is  concerned,  there  Is  no  difference  ^tw«en  the  two 
cases,  in  dealing  with  natural  phenomena,  as  ^  dealing  wl  h 
mind-made  entitles,  we  construct  our  experlmen  al  rnoABlsia 
terms  of  the  Intellectual  standards  of  Identity,  difference,  and 

organisation.  descHption 

8ummary.-Thu8  we  see  that,  so  far  as  ^°«  ""^  J^ 
of  scientific  procedure  Is  concerned,  the  theory  of  ^.lentlflc 
method  resemble,  the  theory  of  Judgment  »"^  ^^-^^-^J^ 
inference.  Sense-perception  furnishes  us  with  he  starting 
*;,nt  for  our  Intellectual  operations,  and  the  intellectual  op^^^- 
atlcns  consist  In  taking  to  pieces  and  ^f  "*°«^»';«  f  "^J^^a^ 
given  m  the  concrete  situation.  In  such  a  way  that  we  obtain 
fnsight  into  Its  laws  and  principles.     This  taking  to  pieces 

Ind  'Arranging  takes  place  by  the  «P-;--^>  ^^^^  ," 
of  mental  models  which  we  then  proceed  to  test  and  verify  by 
r  f^ren^e  to  the  datum.    Compared  with  J"^«--^f^X' 
of  scientific  method  corresponds  approximately  to  the  Add  of 
symbolic  judgment,  and  the  typical  example  o' ^^^J"  ^^^ 
algebraical  wlutlon  of  some  concrete  problem  by  »««"  « 
Simultaneous  equations.    In  symbolic  Judgment,  however   the 
fleTd  seems  perhaps  a  little  wider,  while  the  "dental  modd.  or 
symbol,  of  which  science  makes  use  seem  more  "«tricted  to 
nuantltative  and  causal  models.     The  difference  is.  however. 
Snfy  Ipprrent.    For  though  science  does  make  use  cWefly  o 

theL  two  types  of  symbol  for  '-'r''''^\Z''Z\Xirl 
can  and  does  use  other  models  also,  and  in  principle  Is  pre- 
cisely as  unrestricted  as  is  symbolic  Judgment.2       ^,-^^^,„ 
Comwred  with  Inference,  again,  there  is  but  little  difference. 
BotrpTo^ed\y  analysis  and  synthesis  hy^^^lj-j^*;-  „^^ 
given  situation  and  reconstructing  It  in  the  light  of  Intel 
lectual  standards,  and  both  use  approximately  the  «une  meth- 
ods and  tte  same  standards.    But  the  field  of  Inference  1.  per 
Cllghtly  wider  than  the  field  of  scientific  method,  for  it 

.  Sclentlflc  method  In  practUe  U,-S{'-V^f^,{C.a\'l^«a' ^Mf^^^^ 
values,  anrt  t«ke«  "»  f'T"","*  'letloaf  a^d  r^^^^^  Thl«  l«  becwae 

u  auch— i.  «..  «?|?  *,*J'';^''kem^i^^VM  to  e^^^  »n  terms  of  either 

^"X;\a*^rT.*ul:fmS"' BSt*ln  p?l«clple  they  ma,  «>me  day 
be  a  part  of  aclence. 


3S0 


THEORY  OF  SCIENTIFIC  METHOD 


I 


C. 


eoTen  the  ground  of  ludgmenti  of  experience  also,"  and  even 
—to  iome  slight  extent— the  ground  of  transcendent  Judg- 
menu.  Scientific  method,  however.  Is  rigidly  restricted  to  the 
symbolic  reconstruction  of  Its  data,  and  sharply  distinguishes 
Itself  from  any  attempt  to  transcend  the  field  of  possible  expe- 
rience. It  Is  thus  a  specialised  and  concentrated  application 
of  Inference  to  a  somewhat  narrow  part  of  the  whole  possible 

field. 

Validity   of   Scientific    Method.     (A)    Mind-Made    Entitles. 
—In  the  light  of  our  previous  chapters,  we  can  state  briefly 
the  conditions  of  the  validity  of  scientific  method.    As  we  have 
seen.  It  is  possible  for  scientists  to  make  mistakes.    Analysis 
and  synthesis,  abstraction  and  determination.  Induction  and 
deduction,  of  themselves  are  not  Infallible;  and  as  we  pointed 
out  in  the  chapter  on  Fallacies,  it  is  possible  to  go  astray  even 
in  dealing  with  mind-made  entities.     Owing  to  accidents  of 
educational  environment,  different  people  tend  to  use  slightly 
differing  sets  of  mental  models,  and  it  is  hard  for  A  to  under- 
stand exactly  the  mental  models  of  B.     There  is  thus  in  all 
exposition  a  certain  amount  of  marginal  error,  which  can,  of 
course,  by  careful  attention  be  reduced  to  a  minimum.     But 
when  all  is  said  and  done,  some  slight  difference  between  the 
symbolic  tools  or  models  used  by  A  and  the  mental  Instruments 
used  by  B  tends.  In  practise,  to  remain,  and  is  thus  a  constant 
source  of  error.    But  the  chief  source  of  error  is  undoubtedly 
to  be  sought  in  the  relation  of  the  Intellectual  to  the  sensory 
element.     As  we  saw  in  the  case  of  the  symbolic  Judgment, 
even  in  dealing  with  text-book  problems— which  are  cerUinly 
mind-made  entities— it  is  very  easy,  in  the  preliminary  analy- 
sis and  synthesis  which  gives  us  the  x  and  y  equations,  to 
omit  or  add  something  which,  slight  though  it  may  be  in  it«lf. 
yet  vitiates  in  some  degree  all  subsequent  inferences  and  con- 
clusions.   So  also  in  the  verification,  when  we  come  back  from 
our  deductions  and  compare  these  detailed  consequences  of  our 
mental  model  with  the  details  of  the  concrete  sltuatiM,  It  is 
very  easy  to  overlook  a  few  obstinate  facts  in  favor  af  a  fa» 


» ScWutinc  Dif^hod  aJBO  contsiM  geperallsatlonii  from  nperlenM. 
•.rrlved  it  by  abstrK-tion  and  determination,  and  thun  to  a  allirtit 
SteLt  enteri  the  field  of  experienHal  ludinnent  al«o.  But  Itn  rhWf 
work  ilea  more  In  the  field  of  symbolk-  judgnienf . 


VALIDITY  OF  SCIENTIFIC  METHOD 


3S1 


cinatiDf  theory.*  Thlt  is  eipwsiaMy  Hkrty  ^  h«PP«n  wh«r« 
the  orlflnal  eltuaUon  Is  complex.  These  occMlons  of  error 
are  always  with  us,  and  Inyalldate  a  Urge  percentage  of  our 
attempts  to  apply  scientific  method. 

Still.  In  dealing  with  mind-made  entlUes,  there  Is  no  doubt 
that  we  can  be  entirely  succeMful.  Our  procedure  can  be  both 
obJectlTe  and  complete.  The  conditions  of  lU  validity  are  sim- 
ple, and  are  the  same  as  the  conditions  already  noUced  as 
indispensable  for  validity  in  Judgment  and  in  inference.  The 
sensory  apprehension  must  be  direct,  and  the  Intellectual  con- 
struction must  obey  the  Intellectual  norms  of  Identity,  differ- 
ence,  and  organisation,  and  finally,  the  sensory  and  intellectual 
elements  must  be  brought  together  correctly.  That  this  row  be 
accomplished,  our  success  in  solving  mathematical  problems, 
In  solving  ciphers,  and— In  many  cases— in  solving  ethical, 
esthetical,  and  even  religious  problems,  sufllclently  attests.  In 
dealing  with  entitles  which  are  strictly  mind-made,  complete 
validity  Is  poMlble. 

(B)    NatunU   Phenomena^In   dealing  with   natural   phe- 
nomena, we  have  already  seen  that  complete  and  final  validity 
is  out  of  the  question.    It  is,  however,  possible  that  our  meth* 
ods— «.  0.,  the  mathematical  treatment  of  physical,  psycho- 
logical, and  even  sociological  problems— may  be  valid  as  far 
as  they  go.    On  what  does  their  validity  depend?    It  depends 
upon  the  same  conditions  as  we  discovered  in  discussing  Judg- 
ment and  inference.    So  far  as  the  sensory  apprehension  is 
direct,  it  is  ultimate  and  must  be  accepted.     So  far  as  the 
mental  models  are  framed  strictly  in  accordance  with  intel- 
lectual standards,  they  also  are  ultimate,  and  must  be  accepted. 
Finally,  so  far  as  both  sense  and  Intellect  are  correctly  brought 
to  bear  upon  one  and  the  same  problem,  it  can  so  far  be  solved, 
and  solved  In  a  way  which  is  valid— though  perhaps  it  remains 
Inemnplete.    The  only  adequate  test  of  validity  In  these  cases, 
where  our  sensuous  apprehension  Is  not  perfectly  direct,  and 
our  Intellectual  elforU  seem  confined  to  the  Indirect  trial-and- 
error  method  which  tests  one  menUl  model  after  another 
until   it  approximates  to  discovering  something  which  will 
"work"— to  such  cases  the  only  adequate  test  of  validity  is  the 


4  One  of  the  be«t  known  Inirtance.  In  recent  r**"  •■»»»«  ^JL.^' 

HSlTan  the  «10«i  »e  *fr«d  th«t  It  1«    •brlllUirt.  but  n«»t  conTlnc- 
^y    The  Baconian  view  of  Bhrte-pearc  Is  another  famooa  InstMice. 


V 


1m'    \, 


THHORY  OF  SCIKNTIFIC  METHOD 


352 

advance  of  aclence  Itoelf.  If  our  methoda  not  only  provide  ua 
with  a  fair  aolutlon  of  their  special  problem,  but  are  alao 
found  fruitful  In  other  nelds.  and  of  aaalatance  In  helping  on 
the  advance  of  acence.  they  may  be  looked  upon  as  valid. 

Conclusion.— If  we  look  back  over  the  whole  coarse  of 
our  Inquiries,  we  find  that  the  endeavor  of  man  to  solve  hit 
problems  by  the  use  of  logical  thought,  rather  than  by  trust- 
ing to  instinct  and  feeling.  Is  of  a  very  dettnlte  and  pronounced 
-  character.    Inludgment.  we  Uke  apart  the  given,  sensory  flow 
r  *  experience,  split  it  up  into  elements  which  are  cut  off  and 
fixed  by  the  mind,  and  form  differentiated  identities  out  of 
which  we  proceed  to  build  up  an  Intellectuallsed  model  of  the 
situation  with  which  we  are  dealing.    In  Inference,  we  analyse 
and  expand,  constructing  out  of  precisely  similar  intellectual. 
Ised  elements  whole  edifices  of  thought  whlrn  extend  the  Intel- 
lectually   reliable  aspects  of  our  experleice  almost   without 
I  limit     Finally,  in  scientific  method,  we  reauce  this  framing 
of  mentol  models  to  a  system,  to  the  methodical  application 
of  certain  tested  and  approved  types  of  mental  model,  espe- 
cially of  a  mathematical  character,  in  a  way  which  leads  to 
the  gradual  but  sure  advance  of  scientific  knowledge.    That  is 
to  say.  the  character  of  logical  thought  consists  in  substituting, 
for  the  vague  continuity  of  sensuous  feeling,  the  highly  artifi- 
cial but  thoroughly  determinate  and  exact  menUl  counters 
known  as  concepts. 

With  sensation  and  feeling,  we  cannot  rise  above  the  con- 
crete situation.     We  live  these,  we  experience  these,  we  are 
these.     Sensation,   feeling.    Impulse— these   are  the   stuff   of 
which  life,  as  we  are  conscious  of  living,  is  made  up.    These 
are  what  are  half-revealed  by- introspection,  by  looking  within 
and  attempting-vainly,  as  it  seemsB— to  place  our  finger  upon 
the  pulse  of  consciousness.    They  are  parts  of  the  stream  of 
consciousness,  and  constitute  our  life.    Our  llfe-but  not  our 
knowledge.    We  live  them,  but  cannot  contemplate  and  under- 
stend  them     They  evade  our  mental  grasp,  and  leave  us  vainly 
trying  to  say  many  thinga.     We  graap  at  consciousness,  and 
are  left  with— a  psychological  theory.    We  try  to  apprehend 
the  nature  of  thought,  and  are  left  wlth-a  theory  of  logic. 
The  nature  of  understanding  is.  as  we  say.  not  intuitive  but 
discursive.    It  is  indirect,  and  constructs  Intellectuallsed  entl- 


*Cf.  W.  B.  Piltabary.  FundamrntaU  of  PtychoUttn.  p.  T. 


CONCLUSION 


^V-.-! 
'_>^ 


tiM  Which  »re  tlwayt  •omewhtt  different  from  the  realltlee 
which  they  are  tuppoeed  to  repreeent.  If  we  try  to  under- 
lUnd.  we  InevlUbly  conrtruct  more  or  leu  plausible  thwriet, 
and  Bubetltate  for  the  reality  the  menUl  conatructlon  which 
■eemi  to  explain  It  beet.  What  we  underaUnd  le  thua  always 
primarily  what  our  Intellect  has  Itself  Introduced  Into  the 
phenomena  studied.  The  structure  built  up  In  the  sciences  Is 
a  mind-made  structure,  and  Is  Intelligible  precisely  In  so  far 
as  It  Is  of  the  nature  of  Intellect.  It  Is  of  the  mind.  menUl. 
and  has,  In  relation  to  the  phenomena  which  we  experience, 
an  application  which  Is  only  secondary  and  Indirect. 

At  the  same  time,  there  Is  no  doubt  that  logical  thought  la 
•uccessful.    One  steamer  leaving  the  wharf  a  day  behind  a 
slower  steamer  may  seem  to  have  llttW  to  do  with  algebra, 
and  the  dlsUnt  smoke  on  the  horlson  may  seem  perhaps  to 
have  more  connection  with  poetry  than  with  trigonometry. 
And  yet.  trigonometry  and  algebra  can  give  us  exact  Infor- 
mation as  to  the  distance  of  that  smoke  on  the  horlson  and 
the  hour  at  which  we  shall  pass  the  slower  steamer,  and  that 
information  will  be  found  to  work.     Without  '-ch  menUl 
models,  our  steamer  and  railroad  schedules  would  be  impos- 
itble   and  the  whole  series  of  conventions  and  symbols  upon 
which  our  modern  civilisation  rests  would  vanish  Into  thin 
air     Logical  thought  works.    It  Is  tested  and  found  valid  at 
every  moment  of  our  everyday  life,  as  well  as  In  the  labora- 
tories of  scientists.  ^  ^        ..... 
How  are  we  to  explain  this  validity?    How  Is  It  that  a  mlnl^; 
made  model  will  tell  us  more  about  the  structure  of  reallty> 
than  our  most  Intimate  psychological  experiences?    We  can. 
only  hint  at  an  answer  to  this  InevlUble  problem.    We  can 
account  for  the  success  of  our  mental  models  only  «PO»JP« 
assumption  that  these  represent-at  least  approxlmately-the 
intelligible  structure  of  the  concrete  facU  of  experience,  that 
the  phenomena  of  nature  have  Intelligible  laws,  that  the  unl- 
verse  Is  essentially  rational  or  even  mind-made,  and  tnat  its 
rationality  Is  akin  to  the  rationality  which  we  discover  In  oor 
own  logical  thinking.    It  Is.  In  fine,  only  so  far  as  our  reason 
I,  Identical  In  principle  with  the  reason  embodied  »»«"»«';•*» 
facts,  that  the  unfolding  of  our  own  mental  constructions  «sn 
brlni  us  into  touch  with  the  nature  of  the  universe^   The  fuf^ 
ther  study  of  this  problem  and  of  this  answer  belongs,  not  I 
to  logic,  but  to  metaphytlcB. 


354 


THEORY  OF  SOENTinC  METHOD 


FOR  rDRTHBB  RBADINO 

B.  BoMoquet,  Lot/ie,  Bk.  II,  chapter  vll.  r.  11.  Bnidlcf,  PHmeipltt 
of  Logic,  Bk.  Ill,  Ptrt  II,  chapters  IIMt.  II.  Lotaa.  Lo^to,  Bk.  Ill, 
chapter  t.    Chr.  BIfwart,  Logic.  Vol.  II,  pp.  IMS-M7. 


INDEX  I 


4,    11  n.,   36  n. 
142.     215  n., 


AewhyluB,  361  n. 
Aristotle,  v.  3.  61.  142.  199-200. 
218.  273.  280  n..  283.  296.  337 
Arnold.  122  n. 
Ayer,  142  n. 

Bacon.  211.  361  n. 
Bain.  280-281 
Bakewell.  89  n. 
Benolt.  142  n. 
Bergion.  187  n. 
Binet.  154,  218 
Boluier,  225  n. 
BoMnquet,   v. 
91  n.,     99  n.. 
216  n..  314  n. 
Bradley.  A.  C,  142  n. 
Bradley.  C.  O.,  122  n. 
Bradley.  P.  U.,  ▼.  Hn-  ^^' 
99  n.  102.  146.  188  n..  202  n.. 
327  n..  338 
Bridget,  218  n. 
Brill,  322  n. 
Biichner.  339  n. 

Caird.  143  n. 
Chadwlck,  218  n. 
Coleridge,  302 
Condlllac.  102.  103  n.,  142 
Copernicus.  274 
Cousin,  142  n. 
Cox.  204  n. 

Davles.  178  n. 
Deacartes.  102 
Dewey.  ▼.  264  n. 


Brdman,  y.  11  n..  38  n..  104  n.. 

108 
Euclid,    287-288.    297,    317  n., 

319-320,  324 
Euripides.  191 

Finkelstein.  148  n. 
Piscber,  143  n. 
Freud.  143,  322  n. 
Purneauz.  225  n. 

Oalton,  202  n. 

Ooblot.   176  n..    192  n..    283  n.. 

298  n. 
OoldBcheider,  286  n..  287 
Grant,  142  n. 
Oroos,  81  n. 

Hart.  144  n..  213  n. 
Hartenstein.  142  n. 
Hegel.    4.    102.    143.    161  n., 

228  n..  264,  337 
Hibben,  123  n. 
Hobbes,  111 
Hume,  v..  149  n. 
Huxley,  286  n..  265.  266  n. 

James.    1  n.,    144  n..    278  n., 

286  n. 
Joacbim,  338  n. 
Jones,    A.    L.,    85  n..    226  n., 

235  n.,  266  n. 
Jones.  E.,  143  n..  322  n. 
Jung,  322  n. 

ISS 


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356 


INDKX  I— Continued 


Kant.   V.     .  37,   91  n.,   100  n., 

139.  1'. ;,  143,  218.  246.  253 
Keller.  154 

Leibniz,  102,  292  n. 

Locke.  V.  103  n.,  142-143,  151, 

165.      167,      200  n.,      201  n., 

250  n.,  329  n. 
Lodge,  O.  J..  268  n. 
Lodge,  R.  C.  151  n. 
Lotze.  V,  108,  121  n. 
Lovejoy,  292  n.,  339  n. 
Lully.  292  n. 

MacDougall,  223  n. 

MacLennan,  10  n. 

Marrett,  191  n. 

Meikel.ohn,  91  n..  100  n. 

Mellone,  264  n. 

Menander,  191. 

Mill,  V.  103  n..  123  n.,  125,  133, 

149.  156.  2UZ.  281,  326.  328- 

329 

Nettleshlp,  121  n. 
Newton,  264-265,  266 
Nietzsche,  273 

Pestalozzi,  3 

Peterson,  148  n. 

Pilate,  56 

Plllsbury.  87  n.,  138  n.,  164  n.. 

233  n..  299.  352  n: 
Plato,  V,  3,  90  n..  101,  102. 

112  n..  151.  166,  167,  178  n., 

180,  228  n.,  273.  274.  275  n.. 

323,  330  n.,  341-342 
Plotinus,  89  n. 
Porphyry,  1 56  n. 
Prince.  163  n. 


Royce.  123  n.,  142,  314  n. 
Russell.  145  n..  153  n. 

Schelling.  228  n..  259 
Schuppe.  11  n..  125  n. 
Sellars,  202  n. 
Shakespeare.      143.      189-190, 

351  n. 
Sidgwick.  H.,  88  n. 
Slgwart.  V,  112,  120  n..  125  n., 

128  n. 
Simmel,  338  n. 
Socrates,   109.   110,   112.   140. 

332-333 
Spencer.  206.  227  n..  324.  336. 

338 
Spinoza.  19,  61,  142 
Stout,  174  n.,  250  n. 
Swift.  164 

Tacitus,  225 
Taylor.  A.  E..  81  n. 
Tufts,  254  n. 

Varisco,  161  n.,  340  n. 
Vaughan,  178  n. 
Verrall.  351  n. 

Wilson.  J.  C.  156  n. 
Windelband.  11  n.,  142 
Wolff.  216  n..  247,  259 
Wundt.    V.    2n.,    11  n..    23  n., 

38  n.,  108,  215  n.,  283  n..  336. 

338,  343-345 

Yerkes,  218 
•  Zeno,  274 


Index  II 


i.  «    «fc    -r-rW    11    17  Categorical,  134-136,  172 

Abstraction,  ch.  xxu,  ii,  i*.  -L          on  ^^,a  n    215-216  226- 

30    38,  40,  41,  82.  92.  199-  Cause.  80.  128  ff..  215  21b, 

227 

2®^'  ^^^             .     ..          oftA  —Aristotle's  doctrine.  296 

—and    determination.    260-  — ^^^^'f  °" ,    „.    „.  „;    45 

^"  Certainty,  23.  28,  30-di,  «» 

.   .  „        «f  ^"4  ^^^  —See  also  Validity 

fr°\^rnO    111    lllllS  Chaos.  3,  46-49.  179 

Affirmation    110.  Ill,  U^  c,^,,ifleation.   ch.   xxviii.   11. 

Algebra  of  thought,  v.  29^  ^^    ^^^    ^^^    ^^^206 

^°^!°*f  •  !:L  Till  xix  2  6   9  Clearness.  44-45.  47-49.  52.  76. 

^""o^t'  55    68    71     92    121  179-180.  188.  314 

24.     40,     55,     00.      <1.     3^,     ■^*"^'  _       .„      mn      nn      QO 

159,  W8-199  coherence,  65,  68.  76,  79,  92, 

_„d  ,,«the.I.,  ch.  «1,  220  96^^__  ^^__^^    ^   ^  ^    ^^^ 

!!;^.,  2,.0  .„...,  n2  CO..P.  3.  ,. .. .-.  - 

A  priori,  153,  16b  ' 

Aspiration.  33,  60.  74.  102  205    250    3u2 

Association.    5.    17-30.    40-41  Conclu  ion.  3    4,   25. 

pa.i..  58.  71.  74.  8.-83.  86.  J^^^i^/^//J  3,  ,,,  «. 

.  ^^^     Hon    4   ^33-334  consistency,  6.  37.  39-41.   80, 

Assumption,  4,  SiA-ni  074.075  281 

58,  102,  Ul,  171-172,  u,  3,,  «,  62.«3, 124-125,  181 

Attitude,  logic.!,  1-4  coEtemilatlon,  82,  84 
B.c..o„.d  o,  expenence,  .n-      Co.«x.      -nectua.,     82-80 

Ter;,  17,  XO-2.,  34,  38,      Ooht.n».t,,    ihteUectual,    94, 

*^'  ^^',^^0  K   r:,  -sensory,  25-50  passim,  55. 

Behavior  1.  2.  5.  57  ^^   ^g.  ^^^  ^^   ^^^ 

ir;4S.ce.l7.19  Con-ri^.  .0.  42.  44. 

card-index.  44.  311-312  95.  97.  181.  184.  348 

357 


358 


INDKX   II— Continued 


Deduction,  ch.  xxt,  203 
— and  induction,  ch.  xxvi 

Definition,  ch.  xxvii,  2,  136  n., 
204-205 

Demonstration,  ch.  xxix,  27 

Dependence,  ch.  xii,  120,  177 

Desire,  31,  33,  53 

Determination,  ch.  xxiii,  200 
—and  abstraction,  260-262 

Diagnostic  claesirtv.ation,   312 

Difference,  ch.  vl,  38-46  pas- 
sim, 68,  91,  94 

Discourse,  subject  of,  47-52 
passim 

Discovery,  121  ff.,  135,  156, 
159,  173,  174,  180,  198  ff., 
263  ff. 

Distinction,  11.  18,  37,  38,  41, 
55,  57,  63,  68,  76 

Distraction,  58 

Division,  307,  309,  314 

Dogmatism,  135 

Efficiency,  3,  5,  44,  198,  221 
Error,    ch.    xxx,    24,    28,    43, 

68  n.,  270,  350 
Evidence,  28-30,  130 
Evolution,  2,  6,  104,  235 
Expansion,  analytic,  120-122 
Experimental   Judgments,   12- 

15,  18-19,  21,  25-28,  etc. 
Experiment,  24,  27,  141,  145, 

166 
Explanation,  172,  204-205 
Exposition,  204-207 

Fact,  23,  29 

Faculty  physchoiogy,  250,  334 

Failure  to  judge,  20,  62,  96, 

98,  109-111,  326 

—to  prove,  31,  326 


Faith,  60,  145-146 

Fallacy,  ch.  xxx 

Falsity,  24,  37,  92 

Feeling,   3,   20,   23-24,   33,  38, 

40,  48,  53,  55,  60-63,  68,  70, 

76,  102,  145,  187,  352 
Fiction,  28.  86 
Focus  of  consciousness.  27,  28, 

32,  33,  39,  40,  101 
Form  and  formal,  37,  44,  52, 

88 
Generalisation,  18,  27,  30,  201- 

202,  249-250,  261 
Genetic  method,  6 
Given,  the,  10,  11,  18,  23,  31, 

37,  143.  191.  237-238 
God,  31,  33,  40,  44,  "1,  60,  62, 

74-75,  87-88 
Grammar  and  logic,  7  n..  47-48 
Ground,  logical.  80.  114,  128  ff. 

Happening,   23,   29  n.,   53,  68. 

71,  76,  77 
History.    6.    28-29.    49-50.    85, 

105-106 
Human  experience,  20,  31,  43, 

51-52,  60,  87-88 
Hypothesis,  ch.  xii,  109,  166. 

274 

Idea.  2,  19-20.  31,  38.  43,  51,  52, 

60,  111 
Idealism,  101-102,  143 
Identical  propositions,  55.  59. 

62 
Identity,  ch.  v,  31,  37-45.  54- 

59  passim,  etc. 
Ignorance,  109-112 
Ignoratio  elenchi,  334 
Illusion.  24,  31 
Image,  2.  20,  139 


INDEX  II— Continued 


3S9 


Imagination,  20,  51,  112,  139, 

171 
Impersonal  judgments,  10 
Impressions,    37,    40,   49,    50, 

102 
Index-classlflcation,    44,    311- 

312 
Individuality,  65-66,  69,  77,  92. 

219,  338 
Induction,  ch.  xxlv,  18,  27,  30- 

31,  202-203 

— and  deduction,  ch.   xxvi, 
203 
Inductive  leap,  158 
Inference,  Part   II.  125.   193- 

194 
Infinite,  14,  20.  31,  33.  43.  51, 

88 
Insight,  4.  5.  203,  232.  270.  289 
Instinct,  1-3.  38.  145,  333.  352 
Instruments,  intellectual,  37. 

212,  350 
Intellect,  chs.  iv-ix,  177,  182, 

347-349 

—and  sense,  101  ff.,  182. 184- 

185 
—"pure"  intellect,  15,  102 
Intelligence,  2,  17,  31,  34,  57, 

149,  218.  224 
Interest,  2.  38.  49.  55-56 
Interpretation.  21.  24-25,  27-28, 

30.  40,  95,  105 
Intuition.  93.  121.  143-146,  172 
—mathematical      intuition. 

176 
Inventory.  310-311 
investigation.    198 «..   290-291 
Isolation.  199.  201-202,  249-250 


Judgment,  Part  I 
—defined,  166-167 
—failure  to  Judge,  20,   62, 

96,  98,  109-111,  326 
—field  of,  12-15 
— stages  of.  11-15 


Knowable.  the.  20.  51 
Knowledge.  4,  30,  43,  80,  102. 

109-110,  149 

—latent,  154  fl. 

Laws,  30,  128  ff.,  153,  250.  263 
—of  thought,  4,  6,  37,  39-46. 
52,  91-92 
Logic,  aim  of,  v,  352-353 
— applied,  94 
— and  psychology,  5-6 
—and   natural   science,  80, 

90 
—defined,  5-6,  cf.  23,  352-353 
— modern,  v 
—study  of.  3-5 
—symbolic,  v,  292  n. 
Logical  attitude,  1-4 

Margin  of  consciousness,  27- 

28 
Mathematics.  3-4.  80.  90.  94. 

214-215.  225-226 
Memory,  17,  26,  27 
Mental  counters.  40,  42,  44.  95. 

97.  181.  184,  348 
Metaphysics,  1,  4,  20,  31,  33, 
43,  44,  88.  99,  106,  145,  337, 
353 
Method,    scientific.    Part   III, 

3-5,  103.  135,  142,  145 
Mind,  5,  102,  218 


J60 


Models,  mental,  93,  182,  212- 

213,  258.  269,  278-279.  293-ff.. 

327  ff.,  348  ff. 
MyBticism,  14,  88-89 
Natural  classification,  312-313, 

cf.  294 
Negation,  54,  57,  63,  108-116 
Nervous  system,  38,  333 
Novelty,  ch.  xlv,  39,  57,  122- 

124 

Objective.     24,    109-112,     209, 

223,  269-270 
Organisation,  chs.  vii-viii,  40- 

58  passim,  92,  96 

Perception  and  inference,  124- 

125 
Perceptual    judgments,    9-10, 

17-18,  23-25,  38-40,  46-48,  etc. 
Perfection,  31,  33.  52,  60,  76, 

88 
Personal    experience,    28,    30, 

31,  41,  49,  73 
Personality,  32-33,  43 
Petitio  principii,  333-334 
Phenomena,  102,  223,  271,  291 
Plurality  of  causes,  133-134 
Popular     thought,     133,     136, 

283-284 
Practise  and  theory,  3-5,  135 
Predicate,  logical,  47-55  pas- 
sim 
Premises,  121,  124,  127 
Present,  the.  26-27,  39,  40,  50 
Problems,  human,  1-2,  60,  353 
Proof,    ch.    xxlx,    3,    31,    205, 

206,  314 
Propositions   and   judgments. 

7n. 
Psychology,  5-6,  88,  109,  144, 

146 


INDEX  II--Continued 

Purpose,  65,  77,  209 


Quality  of  sensation,  17,  18, 
21,  34,  244 

Rationalisation,  144 
Reality,  2,  33,  44,  99,  102,  253 
Reason,  20,  37 
Reasonableness,  6,  26,  32,  35 
Reconstruction,  19,  28-31,  42, 

73,  191 
Relations,  39,  65-67,  80,  94.  98. 

102,  108  ff.,  152  ft.,  170,  173- 

174 

Schemata,  142 

Science,  27,  30,  41-46,  58,  80, 

89.  135,  271,  275,  332,  336  ft. 
Selection,  71,  75,  77,  84,  86-87 
Self,  33,  60,  62,  74,  88 

—feeling,  17,  20,  38,  39,  91  n. 
Sensation,  chs.   ii-iii,  37,   47, 

53-56,  76,  93,  102,  149,  169  ft., 

346-347 

— and  judgment,  17  ff. 

—and  intellect,  101  ff.,  182, 
184-185 

— and  validity  of,  ch.  ili 
Sensualism,  102-103 
Simple  judgments,  9-10,  15 
Situation,  concrete,  141,  146, 

170  ft.,  186,  189  ft. 
Standards  of  truth,  5-6,  37-46, 

52,  91-92 
Statistics,  69,  148,  214 
Subject,  logical,  47-55,  passim 
Subjective,  20,  109-112 
Symbolic  judgment,  12-15,  19- 

21,  31-34,  41-42,  49-50,  58-60, 

etc. 

—logic,  V,  292  n. 


INDEX  II— Continued 


361 


SyntheslB,  ch.  xx,  200-201 
— and  analysis,  ch.  xxl 

System     of     Judgments,     ch. 
xxxl,  39-41,   44,  68,  76,  SC- 
SI, S6.  89-92,  95-98 
— nervous  system,  38,  333 

Tabula  rasa,  2,  37-38 
Tests  of  validity,  23-24,  34,  42 
Theory  and  practise,  3-5,  135 
Things-ln-themselves,  31,  187 
Thought,  2-5,  15,  20,  33.  39,  56, 

58.  73-74,  89,  115,  280,  353 
Totality,  65-t»e,  68,  71,  73,  85, 

101,  218-219,  238 
Transcendent  Judgments,  12- 

15,  19-21,  30-34.  42-44.  50-52, 

etc. 


Trial  and  error,  109,  139,  140, 
164,  166,  198,  213,  222,  234 

Truth,  4-6,  14,  23,  28,  37.  41, 
43,  81,  92,  100,  106 

Understanding,  93,  346 

Unity,  28,  39-54  pa««twi,  65-68, 
75-80,  91,  etc. 

Universals,  40-42 

Validity,  chs.  ill,  Ix,  x,  xvil, 

350-353 
Values,  practical,  4,  38,  82,  88, 

188,  339 

—social,  65-66 

—theoretical,  23,  27,  339 
Verification,    27-28,   31,   34-35, 

93,    105.    176-177.    193.    203, 

266 

Words.  19,  20,  58,  187,  292 


i 

i  , 

!     i 


